//------------------------------------------------------------------------------
// CHOLMOD/Include/cholmod.h: include file for CHOLMOD
//------------------------------------------------------------------------------

// CHOLMOD/Include/cholmod.h.  Copyright (C) 2005-2023, Timothy A. Davis.
// All Rights Reserved.

// Each Module of CHOLMOD has its own license, and a shared cholmod.h file.

// CHOLMOD/Check:      SPDX-License-Identifier: LGPL-2.1+
// CHOLMOD/Cholesky:   SPDX-License-Identifier: LGPL-2.1+
// CHOLMOD/Utility:    SPDX-License-Identifier: LGPL-2.1+
// CHOLMOD/Partition:  SPDX-License-Identifier: LGPL-2.1+

// CHOLMOD/Demo:       SPDX-License-Identifier: GPL-2.0+
// CHOLMOD/GPU:        SPDX-License-Identifier: GPL-2.0+
// CHOLMOD/MATLAB:     SPDX-License-Identifier: GPL-2.0+
// CHOLMOD/MatrixOps:  SPDX-License-Identifier: GPL-2.0+
// CHOLMOD/Modify:     SPDX-License-Identifier: GPL-2.0+
// CHOLMOD/Supernodal: SPDX-License-Identifier: GPL-2.0+
// CHOLMOD/Tcov:       SPDX-License-Identifier: GPL-2.0+

//------------------------------------------------------------------------------
// CHOLMOD consists of a set of Modules, each with their own Copyright and
// license: either LGPL-2.1+ or GPL-2.0+.  This cholmod.h file includes
// definitions of the CHOLMOD API for all Modules, and this cholmod.h file
// itself is provided to you with a permissive license (Apache-2.0).  You are
// permitted to provide the hooks for an optional interface to CHOLMOD in a
// non-GPL/non-LGPL code, without requiring you to agree to the GPL/LGPL
// license of the Modules, as long as you don't use the *.c files in the
// relevant Modules.  The Modules themselves can only be functional if their
// GPL or LGPL licenses are used, or if you obtain a different license from the
// respective copyright holders.
//
// For the files in CHOLMOD/Include:
// CHOLMOD/Include/cholmod.h            SPDX-License-Identifier: Apache-2.0
// CHOLMOD/Include/cholmod_internal.h   SPDX-License-Identifier: Apache-2.0
// CHOLMOD/Include/cholmod_template.h   SPDX-License-Identifier: Apache-2.0
// CHOLMOD/Include/cholmod_types.h      SPDX-License-Identifier: Apache-2.0
//
// The Modify Module is co-authored by William W. Hager.
//
// Acknowledgements:  this work was supported in part by the National Science
// Foundation (NFS CCR-0203270 and DMS-9803599), and a grant from Sandia
// National Laboratories (Dept. of Energy) which supported the development of
// CHOLMOD's Partition Module.
// -----------------------------------------------------------------------------

#ifndef CHOLMOD_H
#define CHOLMOD_H

//------------------------------------------------------------------------------
// CHOLMOD conventions
//------------------------------------------------------------------------------

// Each routine in CHOLMOD follows the following conventions:
//
// Naming convention:
// ------------------
//
//  All routine names, data types, and CHOLMOD library files use the cholmod_
//  prefix.  All macros and other #define's use the CHOLMOD prefix.
//
// Return value:
// -------------
//
//  Most CHOLMOD routines return an int (TRUE (1) if successful, or FALSE
//      (0) otherwise.  An int32_t, int64_t, double, or float return value
//      is >= 0 if successful, or -1 otherwise.  A size_t return value
//      is > 0 if successful, or 0 otherwise.
//
//      If a routine returns a pointer, it is a pointer to a newly allocated
//      object or NULL if a failure occured, with one exception.  cholmod_free
//      always returns NULL.
//
// "Common" parameter:
// ------------------
//
//  The last parameter in all CHOLMOD routines is a pointer to the CHOLMOD
//  "Common" object.  This contains control parameters, statistics, and
//  workspace used between calls to CHOLMOD.  It is always an input/output
//  parameter.
//
// Input, Output, and Input/Output parameters:
// -------------------------------------------
//
//  Input parameters are listed first.  They are not modified by CHOLMOD.
//
//  Input/output are listed next.  They must be defined on input, and
//  are modified on output.
//
//  Output parameters are listed next.  If they are pointers, they must
//  point to allocated space on input, but their contents are not defined
//  on input.
//
//  Workspace parameters appear next.  They are used in only two routines
//  in the Supernodal module.
//
//  The cholmod_common *Common parameter always appears as the last
//  parameter.  It is always an input/output parameter.

//------------------------------------------------------------------------------
// CHOLMOD matrix formats
//------------------------------------------------------------------------------

// A CHOLMOD sparse, dense, or triplet matrix A, or a sparse factorization L
// can hold numeric values of 8 different types, according to its A->xtype and
// A->dtype parameters (or L->xtype and L->dtype for a sparse factor object).
// These values are held in the A->x array, and also A->z for "zomplex"
// matrices.
//
//  A->xtype:   the matrix is real, complex, "zomplex", or pattern-only.
//
//      (0): CHOLMOD_PATTERN:   A->x and A->z are NULL.  The matrix has no
//                              numerical values.  Only the pattern is stored.
//
//      (1): CHOLMOD_REAL:      The matrix is real, and the values are held in
//                              A->x, whose size (in terms of double or float
//                              values) is given by A->nzmax.  The kth value in
//                              the matrix is held in A->x [k].
//
//      (2): CHOLMOD_COMPLEX:   The matrix is complex, with interleaved real and
//                              imaginary parts.  The kth value in the matrix
//                              is held in A->x [2*k] and A->x [2*k+1], where
//                              A->x can hold up to 2*A->nzmax values.
//
//      (3): CHOLMOD_ZOMPLEX:   The matrix is complex, with separate array for
//                              the real and imaginary parts.  The kth value in
//                              the matrix is held in A->x [k] and A->z [k],
//                              where A->x and A->z can hold up to A->nzmax
//                              values each.

    // A->xtype values:
    #define CHOLMOD_PATTERN 0
    #define CHOLMOD_REAL    1
    #define CHOLMOD_COMPLEX 2
    #define CHOLMOD_ZOMPLEX 3

//  A->dtype:   this parameter determines the type of values in A->x (and A->z
//              if zomplex).
//
//      (0) CHOLMOD_DOUBLE:     A->x (and A->z for zomplex matrices) is double.
//                              If A is real, A->x has a size of A->nzmax *
//                              sizeof (double).  If A is complex, A->x has
//                              size A->nzmax * 2 * sizeof (double).  If
//                              zomplex, both A->x and A->z have size A->nzmax
//                              * sizeof (double).
//
//      (4) CHOLMOD_SINGLE:     A->x (and A->z for zomplex matrices) is float.
//                              If A is real, A->x has a size of A->nzmax *
//                              sizeof (float).  If A is complex, A->x has size
//                              A->nzmax * 2 * sizeof (float).  If zomplex,
//                              both A->x and A->z have size A->nzmax * sizeof
//                              (float).  This feature is new to CHOLMOD v5.
//

    // A->dtype values:
    #define CHOLMOD_DOUBLE 0
    #define CHOLMOD_SINGLE 4

// Unless stated otherwise, the xtype and dtypes of all inputs to a method must
// be the same.
//
// Many methods accept an xdtype parameter, which is simply xtype + dtype,
// combining the two parameters into a single number handling all 8 cases:
//
//      (0) CHOLMOD_DOUBLE + CHOLMOD_PATTERN    a pattern-only matrix
//      (1) CHOLMOD_DOUBLE + CHOLMOD_REAL       a double real matrix
//      (2) CHOLMOD_DOUBLE + CHOLMOD_COMPLEX    a double complex matrix
//      (3) CHOLMOD_DOUBLE + CHOLMOD_ZOMPLEX    a double zomplex matrix
//      (4) CHOLMOD_SINGLE + CHOLMOD_PATTERN    a pattern-only matrix
//      (5) CHOLMOD_SINGLE + CHOLMOD_REAL       a float real matrix
//      (6) CHOLMOD_SINGLE + CHOLMOD_COMPLEX    a float complex matrix
//      (7) CHOLMOD_SINGLE + CHOLMOD_ZOMPLEX    a float zomplex matrix
//
// This approach was selected for backward compatibility with CHOLMOD v4 and
// earlier, where only the first four values were supported, and where the
// parameter was called "xtype" instead of "xdtype".  Several function names
// reflect the older parameter name (cholmod_*_xtype), but they have not been
// renamed "_xdtype", for backward compatibility.
//
// A CHOLMOD sparse or triplet matrix A can held in three symmetry formats
// according to its A->stype parameter.  Dense matrices do not have this
// parameter and are always treated as unsymmetric.  A sparse factor object L
// is always held in lower triangular form, with no entries ever held in the
// strictly upper triangular part.
//
//      0:  the matrix is unsymmetric with both lower and upper parts stored.
//
//      <0: the matrix is symmetric, with just the lower triangular part and
//          diagonal stored.  Any entries in the upper part are ignored.
//
//      >0: the matrix is symmetric, with just the upper triangular part stored
//          and diagonal.  Any entries in the upper part are ignored.
//
// If a sparse or triplet matrix A is complex or zomplex, most methods treat
// the matrix as Hermitian, where A(i,j) is the complex conjugate of A(j,i),
// when i is not equal to j.  Some methods can also interpret the matrix as
// complex symmetric, where A(i,j) == A(j,i) when i != j.  This is not
// determined by the matrix itself, but by a "mode" parameter of the function.
// This mode parameter also determines if the values of any matrix are to be
// ignored entirely, in which case only the pattern is operated on.  Any output
// matrix will have an xtype of CHOLMOD_PATTERN.
//
// The valid mode values are given below, except that many methods do not
// handle the negative cases.  Values below the range accepted by the method
// are treated as its lowest accepted value, and values above the range
// accepted by the method are treated as its highest accepted value.
//
//  mode = 2:   the numerical values of a real, complex, or zomplex matrix are
//              handled.  If the matrix is complex or zomplex, an entry A(i,j)
//              that not stored (or in the ignored part) is treated as the
//              complex conjugate of A (j,i).  Use this mode to treat a
//              complex or zomplex matrix as Hermitian.
//
//  mode = 1:   the numerical values of a real, complex, or zomplex matrix are
//              handled.  If the matrix is complex or zomplex, an entry A(i,j)
//              that not stored (or in the ignored part) is treated as equal A
//              (j,i).  Use this mode to treat a complex or zomplex matrix as
//              complex symmetric.
//
//  mode = 0:   the numerical values are ignored.  Any output matrix will have
//              an xtype of CHOLMOD_PATTERN.  This mode allows inputs to have
//              different dtypes.
//
//  mode = -1:  the same as mode = 0, except that the diagonal entries are
//              ignored, and do not appear in any output matrix.
//
//  mode = -2:  the same as mode = -1, except that the output matrix is given an
//              additional slack space so that it can hold about 50% more
//              entries.  This mode is documented here but it is primarily
//              meant for internal use, for CHOLMOD's interface to the AMD,
//              CAMD, COLAMD, and CCOLAMD ordering methods.
//
// The integer arrays in all objects are either int32 or int64, as determined
// by A->type.  This integer type must be identical for all inputs, and must
// also match both the function name (cholmod_method for int32, or
// cholmod_l_method for int64) and the Common->itype as defined when CHOLMOD
// was initialized (via cholmod_start for int32, or cholmod_l_start for int64).

    // itype values:
    #define CHOLMOD_INT  0    /* int32, for cholmod_* methods (no _l_) */
    #define CHOLMOD_LONG 2    /* int64, for cholmod_l_* methods        */

//------------------------------------------------------------------------------
// version control
//------------------------------------------------------------------------------

#define CHOLMOD_DATE "Jan 20, 2024"
#define CHOLMOD_MAIN_VERSION   5
#define CHOLMOD_SUB_VERSION    2
#define CHOLMOD_SUBSUB_VERSION 0

#define CHOLMOD_VER_CODE(main,sub) SUITESPARSE_VER_CODE(main,sub)
#define CHOLMOD_VERSION CHOLMOD_VER_CODE(5,2)
#define CHOLMOD_HAS_VERSION_FUNCTION

#ifdef __cplusplus
extern "C" {
#endif

int cholmod_version     // returns CHOLMOD_VERSION, defined above
(
    // if version is not NULL, then cholmod_version returns its contents as:
    // version [0] = CHOLMOD_MAIN_VERSION
    // version [1] = CHOLMOD_SUB_VERSION
    // version [2] = CHOLMOD_SUBSUB_VERSION
    int version [3]
) ;
int cholmod_l_version (int version [3]) ;

#ifdef __cplusplus
}
#endif

//------------------------------------------------------------------------------
// Large file support
//------------------------------------------------------------------------------

// CHOLMOD assumes large file support.  If problems occur, compile with
// -DNLARGEFILE

// Definitions required for large file I/O, which must come before any other
// #includes.  These are not used if -DNLARGEFILE is defined at compile time.
// Large file support may not be portable across all platforms and compilers;
// if you encounter an error here, compile your code with -DNLARGEFILE.  In
// particular, you must use -DNLARGEFILE for MATLAB 6.5 or earlier (which does
// not have the io64.h include file).

// skip all of this if NLARGEFILE is defined at the compiler command line
#ifndef NLARGEFILE
    #if defined(MATLAB_MEX_FILE) || defined(MATHWORKS)
        // CHOLMOD compiled as a MATLAB mexFunction, or for use in MATLAB
        #include "io64.h"
    #else
        // CHOLMOD is being compiled in a stand-alone library
        #undef  _LARGEFILE64_SOURCE
        #define _LARGEFILE64_SOURCE
        #undef  _FILE_OFFSET_BITS
        #define _FILE_OFFSET_BITS 64
    #endif
#endif

//------------------------------------------------------------------------------
// SuiteSparse_config: definitions for all SuiteSparse packages
//------------------------------------------------------------------------------

#include "SuiteSparse_config.h"

#define CHOLMOD__VERSION SUITESPARSE__VERCODE(5,2,0)
#if !defined (SUITESPARSE__VERSION) || \
    (SUITESPARSE__VERSION < SUITESPARSE__VERCODE(7,6,0))
#error "CHOLMOD 5.2.0 requires SuiteSparse_config 7.6.0 or later"
#endif

//------------------------------------------------------------------------------
// CHOLMOD configuration
//------------------------------------------------------------------------------

// You do not have to edit any CHOLMOD files to compile and install CHOLMOD.
// However, if you do not use all of CHOLMOD's modules, you need to compile
// with the appropriate flag, or edit this file to add the appropriate #define.
//
// Compiler flags for CHOLMOD
//
// -DNCHECK         do not include the Check module.
// -DNCHOLESKY      do not include the Cholesky module.
// -DNPARTITION     do not include the Partition module.
// -DNCAMD          do not include the interfaces to CAMD,
//                  CCOLAMD, CSYMAND in Partition module.
// -DNMATRIXOPS     do not include the MatrixOps module.
// -DNMODIFY        do not include the Modify module.
// -DNSUPERNODAL    do not include the Supernodal module.
//
// -DNPRINT         do not print anything
//
// The Utility Module is always included in the CHOLMOD library.

// Use the compiler flag, or uncomment the definition(s), if you want to use
// one or more non-default installation options:

//      #define NCHECK
//      #define NCHOLESKY
//      #define NCAMD
//      #define NPARTITION
//      #define NMATRIXOPS
//      #define NMODIFY
//      #define NSUPERNODAL
//      #define NPRINT
//      #define NGPL

// The NGPL option disables the MatrixOps, Modify, and Supernodal modules.  The
//  existence of this #define here, and its use in these 3 modules, does not
//  affect the license itself; see CHOLMOD/Doc/License.txt for your actual
//  license.

#ifdef NGPL
    #undef  NMATRIXOPS
    #define NMATRIXOPS
    #undef  NMODIFY
    #define NMODIFY
    #undef  NSUPERNODAL
    #define NSUPERNODAL
#endif

//==============================================================================
// CHOLMOD:Utility Module
//==============================================================================

// the CHOLMOD:Utility Module is always required
#if 1

//------------------------------------------------------------------------------
// CUDA BLAS
//------------------------------------------------------------------------------

// Define buffering parameters for GPU processing
#ifndef SUITESPARSE_GPU_EXTERN_ON
#ifdef CHOLMOD_HAS_CUDA
#include <cublas_v2.h>
#endif
#endif

#define CHOLMOD_DEVICE_SUPERNODE_BUFFERS 6
#define CHOLMOD_HOST_SUPERNODE_BUFFERS 8
#define CHOLMOD_DEVICE_STREAMS 2

//------------------------------------------------------------------------------
// CHOLMOD objects
//------------------------------------------------------------------------------

// CHOLMOD object enums
#define CHOLMOD_COMMON  0   /* parameters, statistics, and workspace */
#define CHOLMOD_SPARSE  1   /* a sparse matrix in CSC form (and variants) */
#define CHOLMOD_FACTOR  2   /* a sparse factorization */
#define CHOLMOD_DENSE   3   /* a dense matrix in column-oriented form */
#define CHOLMOD_TRIPLET 4   /* a sparse matrix in triplet form */

//------------------------------------------------------------------------------
// CHOLMOD Common object
//------------------------------------------------------------------------------

#ifdef __cplusplus
extern "C" {
#endif

typedef struct cholmod_common_struct
{

    //--------------------------------------------------------------------------
    // primary parameters for factorization and update/downdate
    //--------------------------------------------------------------------------

    double dbound ; // Bounds the diagonal entries of D for LDL'
        // factorization and update/downdate/rowadd.  Entries outside this
        // bound are replaced with dbound.  Default: 0.  dbound is used for
        // double precision factorization only.  See sbound for single
        // precision factorization.

    double grow0 ;      // default: 1.2
    double grow1 ;      // default: 1.2
    size_t grow2 ;      // default: 5
        // Initial space for simplicial factorization is max(grow0,1) times the
        // required space.  If space is exhausted, L is grown by max(grow0,1.2)
        // times the required space.  grow1 and grow2 control how each column
        // of L can grow in an update/downdate; if space runs out, then
        // grow1*(required space) + grow2 is allocated.

    size_t maxrank ;    // maximum rank for update/downdate.  Valid values are
        // 2, 4, and 8.  Default is 8.  If a larger update/downdate is done, it
        // is done in steps of maxrank.

    double supernodal_switch ;  // default: 40
    int supernodal ;            // default: CHOLMOD_AUTO.
        // Controls supernodal vs simplicial factorization.  If
        // Common->supernodal is CHOLMOD_SIMPLICIAL, a simplicial factorization
        // is always done; if CHOLMOD_SUPERNODAL, a supernodal factorization is
        // always done.  If CHOLMOD_AUTO, then a simplicial factorization is
        // down if flops/nnz(L) < Common->supernodal_switch.

        #define CHOLMOD_SIMPLICIAL 0 /* always use simplicial method         */
        #define CHOLMOD_AUTO       1 /* auto select simplicial vs supernodal */
        #define CHOLMOD_SUPERNODAL 2 /* always use supernoda method          */

    int final_asis ;    // if true, other final_* parameters are ignored,
        // except for final_pack and the factors are left as-is when done.
        // Default: true.

    int final_super ;   // if true, leave factor in supernodal form.
        // if false, convert to simplicial.  Default: true.

    int final_ll ;      // if true, simplicial factors are converted to LL',
        // otherwise left as LDL.  Default: false.

    int final_pack ;    // if true, the factorize are allocated with exactly
        // the space required.  Set this to false if you expect future
        // updates/downdates (giving a little extra space for future growth),
        // Default: true.

    int final_monotonic ;   // if true, columns are sorted when done, by
        // ascending row index.  Default: true.

    int final_resymbol ;    // if true, a supernodal factorization converted
        // to simplicial is reanalyzed, to remove zeros added for relaxed
        // amalgamation.  Default: false.

    double zrelax [3] ; size_t nrelax [3] ;
        // The zrelax and nrelax parameters control relaxed supernodal
        // amalgamation,  If ns is the # of columns in two adjacent supernodes,
        // and z is the fraction of zeros in the two supernodes if merged, then
        // the two supernodes are merged if any of the 5 following condition
        // are true:
        //
        //      no new zero entries added if the two supernodes are merged
        //      (ns <= nrelax [0])
        //      (ns <= nrelax [1] && z < zrelax [0])
        //      (ns <= nrelax [2] && z < zrelax [1])
        //      (z < zrelax [2])
        //
        // With the defaults, the rules become:
        //
        //      no new zero entries added if the two supernodes are merged
        //      (ns <=  4)
        //      (ns <= 16 && z < 0.8)
        //      (ns <= 48 && z < 0.1)
        //      (z < 0.05)

    int prefer_zomplex ;    // if true, and a complex system is solved,
        // X is returned as zomplex (with two arrays, one for the real part
        // and one for the imaginary part).  If false, then X is returned as
        // a single array with interleaved real and imaginary parts.
        // Default: false.

    int prefer_upper ;  // if true, then a preference is given for holding
        // a symmetric matrix by just its upper triangular form.  This gives
        // the best performance by the CHOLMOD analysis and factorization
        // methods.  Only used by cholmod_read.  Default: true.

    int quick_return_if_not_posdef ;    // if true, a supernodal factorization
        // returns immediately if it finds the matrix is not positive definite.
        // If false, the failed supernode is refactorized, up to but not
        // including the failed column (required by MATLAB).

    int prefer_binary ; // if true, cholmod_read_triplet converts a symmetric
        // pattern-only matrix to a real matrix with all values set to 1.
        // if false, diagonal entries A(k,k) are set to one plus the # of
        // entries in row/column k, and off-diagonals are set to -1.
        // Default: false.

    //--------------------------------------------------------------------------
    // printing and error handling options
    //--------------------------------------------------------------------------

    int print ;     // print level.  Default is 3.
    int precise ;   // if true, print 16 digits, otherwise 5. Default: false.

    int try_catch ; // if true, ignore errors (CHOLMOD is assumed to be inside
        // a try/catch block.  No error messages are printed and the
        // error_handler function is not called.  Default: false.

    void (*error_handler) (int status, const char *file, int line,
        const char *message) ;
        // User error handling routine; default is NULL.
        // This function is called if an error occurs, with parameters:
        // status: the Common->status result.
        // file: filename where the error occurred.
        // line: line number where the error occurred.
        // message: a string that describes the error.

    //--------------------------------------------------------------------------
    // ordering options
    //--------------------------------------------------------------------------

    // CHOLMOD can try many ordering options and then pick the best result it
    // finds.  The default is to use one or two orderings: the user's
    // permutation (if given), and AMD.

    // Common->nmethods is the number of methods to try.  If the
    // Common->method array is left unmodified, the methods are:

    // (0) given (skipped if no user permutation)
    // (1) amd
    // (2) metis
    // (3) nesdis with defaults (CHOLMOD's nested dissection, based on METIS)
    // (4) natural
    // (5) nesdis: stop at subgraphs of 20000 nodes
    // (6) nesdis: stop at subgraphs of 4 nodes, do not use CAMD
    // (7) nesdis: no pruning on of dense rows/cols
    // (8) colamd

    // To use all 9 of the above methods, set Common->nmethods to 9.  The
    // analysis will take a long time, but that might be worth it if the
    // ordering will be reused many many times.

    // Common->nmethods and Common->methods can be revised to use a different
    // set of orderings.  For example, to use just a single method
    // (AMD with a weighted postordering):
    //
    //      Common->nmethods = 1 ;
    //      Common->method [0].ordering = CHOLMOD_AMD ;
    //      Common->postorder = TRUE ;
    //
    //

    int nmethods ;  // Number of methods to try, default is 0.
        // The value of 0 is a special case, and tells CHOLMOD to use the user
        // permutation (if not NULL) and then AMD.  Next, if fl is lnz are the
        // flop counts and number of nonzeros in L as found by AMD, then the
        // this ordering is used if fl/lnz < 500 or lnz/anz < 5, where anz is
        // the number of entries in A.  If this condition fails, METIS is tried
        // as well.
        //
        // Otherwise, if Common->nmethods > 0, then the methods defined by
        // Common->method [0 ... Common->nmethods-1] are used.

    int current ;   // The current method being tried in the analysis.
    int selected ;  // The selected method: Common->method [Common->selected]

    // The Common->method parameter is an array of structs that defines up
    // to 9 methods:
    struct cholmod_method_struct
    {

        //----------------------------------------------------------------------
        // statistics from the ordering
        //----------------------------------------------------------------------

        double lnz ;    // number of nonzeros in L
        double fl ;     // Cholesky flop count for this ordering (each
            // multiply and each add counted once (doesn't count complex
            // flops).

        //----------------------------------------------------------------------
        // ordering parameters:
        //----------------------------------------------------------------------

        double prune_dense ;    // dense row/col control.  Default: 10.
            // Rows/cols with more than max (prune_dense*sqrt(n),16) are
            // removed prior to orderingm and placed last.  If negative,
            // only completely dense rows/cols are removed.  Removing these
            // rows/cols with many entries can speed up the ordering, but
            // removing too many can reduce the ordering quality.
            //
            // For AMD, SYMAMD, and CSYMAMD, this is the only dense row/col
            // parameter.  For COLAMD and CCOLAMD, this parameter controls
            // how dense columns are handled.

        double prune_dense2 ;   // dense row control for COLAMD and CCOLAMD.
            // Default -1.  When computing the Cholesky factorization of AA'
            // rows with more than max(prune_dense2*sqrt(n),16) entries
            // are removed prior to ordering.  If negative, only completely
            // dense rows are removed.

        double nd_oksep ;   // for CHOLMOD's nesdis method. Default 1.
            // A node separator with nsep nodes is discarded if
            // nsep >= nd_oksep*n.

        double other_1 [4] ;    // unused, for future expansion

        size_t nd_small ;   // for CHOLMOD's nesdis method. Default 200.
            // Subgraphs with fewer than nd_small nodes are not partitioned.

        double other_2 [4] ;    // unused, for future expansion

        int aggressive ;    // if true, AMD, COLAMD, SYMAMD, CCOLAMD, and
            // CSYMAMD perform aggresive absorption.  Default: true

        int order_for_lu ;  // Default: false.  If the CHOLMOD analysis/
            // ordering methods are used as an ordering method for an LU
            // factorization, then set this to true.  For use in a Cholesky
            // factorization by CHOLMOD itself, never set this to true.

        int nd_compress ;   // if true, then the graph and subgraphs are
            // compressed before partitioning them in CHOLMOD's nesdis
            // method.  Default: true.

        int nd_camd ;   // if 1, then CHOLMOD's nesdis is followed by
            // CAMD.  If 2: followed by CSYMAMD.  If nd_small is very small,
            // then use 0, which skips CAMD or CSYMAMD.  Default: 1.

        int nd_components ; // CHOLMOD's nesdis can partition a graph and then
            // find that the subgraphs are unconnected.  If true, each of these
            // components is partitioned separately.  If false, the whole
            // subgraph is partitioned.  Default: false.

        int ordering ;  // ordering method to use:

            #define CHOLMOD_NATURAL     0 /* no preordering                   */
            #define CHOLMOD_GIVEN       1 /* user-provided permutation        */
            #define CHOLMOD_AMD         2 /* AMD: approximate minimum degree  */
            #define CHOLMOD_METIS       3 /* METIS: mested dissection         */
            #define CHOLMOD_NESDIS      4 /* CHOLMOD's nested dissection      */
            #define CHOLMOD_COLAMD      5 /* AMD for A, COLAMD for AA' or A'A */
            #define CHOLMOD_POSTORDERED 6 /* natural then postordered         */

        size_t other_3 [4] ;    // unused, for future expansion

    }
    #define CHOLMOD_MAXMETHODS 9    /* max # of methods in Common->method */
    method [CHOLMOD_MAXMETHODS + 1] ;

    int postorder ; // if true, CHOLMOD performs a weighted postordering
        // after its fill-reducing ordering, which improves supernodal
        // amalgamation.  Has no effect on flop count or nnz(L).
        // Default: true.

    int default_nesdis ;    //  If false, then the default ordering strategy
        // when Common->nmethods is zero is to try the user's permutation
        // if given, then AMD, and then METIS if the AMD ordering results in
        // a lot of fill-in.  If true, then nesdis is used instead of METIS.
        // Default: false.

    //--------------------------------------------------------------------------
    // METIS workarounds
    //--------------------------------------------------------------------------

    // These workarounds were put into place for METIS 4.0.1.  They are safe
    // to use with METIS 5.1.0, but they might not longer be necessary.

    double metis_memory ;   // default: 0.  If METIS terminates your
        // program when it runs out of memory, try 2, or higher.
    double metis_dswitch ;  // default: 0.66
    size_t metis_nswitch ;  // default: 3000
        // If a matrix has n > metis_nswitch and a density (nnz(A)/n^2) >
        // metis_dswitch, then METIS is not used.

    //--------------------------------------------------------------------------
    // workspace
    //--------------------------------------------------------------------------

    // This workspace is kept in the CHOLMOD Common object.  cholmod_start
    // sets these arrays to NULL, and cholmod_finish frees them.

    size_t nrow ;       // Flag has size nrow, Head has size nrow+1
    int64_t mark ;      // Flag is cleared if Flag [0..nrow-1] < mark.
    size_t iworksize ;  // size of Iwork, in Ints (int32 or int64).
                        // This is at most 6*nrow + ncol.
    size_t xworkbytes ; // size of Xwork, in bytes.
        // NOTE: in CHOLMOD v4 and earlier, this variable was called xworksize,
        // and was in terms of # of doubles, not # of bytes.

    void *Flag ;    // size nrow.  If this is "cleared" then
        // Flag [i] < mark for all i = 0:nrow-1.  Flag is kept cleared between
        // calls to CHOLMOD.

    void *Head ;    // size nrow+1.  If Head [i] = EMPTY (-1) then that
        // entry is "cleared".  Head is kept cleared between calls to CHOLMOD.

    void *Xwork ;   // a double or float array.  It has size nrow for most
        // routines, or 2*nrow if complex matrices are being handled.
        // It has size 2*nrow for cholmod_rowadd/rowdel, and maxrank*nrow for
        // cholmod_updown, where maxrank is 2, 4, or 8.  Xwork is kept all
        // zero between calls to CHOLMOD.

    void *Iwork ;   // size iworksize integers (int32's or int64's).
        // Uninitialized integer workspace, of size at most 6*nrow+ncol.

    int itype ;     // cholmod_start (for int32's) sets this to CHOLMOD_INT,
        // and cholmod_l_start sets this to CHOLMOD_LONG.  It defines the
        // integer sizes for th Flag, Head, and Iwork arrays, and also
        // defines the integers for all objects created by CHOLMOD.
        // The itype of the Common object must match the function name
        // and all objects passed to it.

    int other_5 ;   // unused: for future expansion

    int no_workspace_reallocate ;   // an internal flag, usually false.
        // This is set true to disable any reallocation of the workspace
        // in the Common object.

    //--------------------------------------------------------------------------
    // statistics
    //--------------------------------------------------------------------------

    int status ;    // status code (0: ok, negative: error, pos: warning)

        // Common->status for error handling: 0 is ok, negative is a fatal
        // error, and positive is a warning
        #define CHOLMOD_OK            (0)
        #define CHOLMOD_NOT_INSTALLED (-1) /* module not installed          */
        #define CHOLMOD_OUT_OF_MEMORY (-2) /* malloc/calloc/realloc failed  */
        #define CHOLMOD_TOO_LARGE     (-3) /* integer overflow              */
        #define CHOLMOD_INVALID       (-4) /* input invalid                 */
        #define CHOLMOD_GPU_PROBLEM   (-5) /* CUDA error                    */
        #define CHOLMOD_NOT_POSDEF    (1)  /* matrix not positive definite  */
        #define CHOLMOD_DSMALL        (2)  /* diagonal entry very small     */

    double fl ;     // flop count from last analysis
    double lnz ;    // nnz(L) from last analysis
    double anz ;    // in last analysis: nnz(tril(A)) or nnz(triu(A)) if A
                    // symmetric, or tril(A*A') if A is unsymmetric.
    double modfl ;  // flop count from last update/downdate/rowadd/rowdel,
                    // not included the flops to revise the solution to Lx=b,
                    // if that was performed.

    size_t malloc_count ;   // # of malloc'd objects not yet freed
    size_t memory_usage ;   // peak memory usage in bytes
    size_t memory_inuse ;   // current memory usage in bytes

    double nrealloc_col ;   // # of column reallocations
    double nrealloc_factor ;// # of factor reallocations due to col. reallocs
    double ndbounds_hit ;   // # of times diagonal modified by dbound

    double rowfacfl ;       // flop count of cholmod_rowfac
    double aatfl ;          // flop count to compute A(:,f)*A(:,f)'

    int called_nd ; // true if last analysis used nesdis or METIS.
    int blas_ok ;   // true if no integer overflow has occured when trying to
        // call the BLAS.  The typical BLAS library uses 32-bit integers for
        // its input parameters, even on a 64-bit platform.  CHOLMOD uses int64
        // in its cholmod_l_* methods, and these must be typecast to the BLAS
        // integer.  If integer overflow occurs, this is set false.

    //--------------------------------------------------------------------------
    // SuiteSparseQR control parameters and statistics
    //--------------------------------------------------------------------------

    // SPQR uses the CHOLMOD Common object for its control and statistics.
    // These parameters are not used by CHOLMOD itself.

    // control parameters:
    double SPQR_grain ;     // task size is >= max (total flops / grain)
    double SPQR_small ;     // task size is >= small
    int SPQR_shrink ;       // controls stack realloc method
    int SPQR_nthreads ;     // number of TBB threads, 0 = auto

    // statistics:
    double SPQR_flopcount ;         // flop count for SPQR
    double SPQR_analyze_time ;      // analysis time in seconds for SPQR
    double SPQR_factorize_time ;    // factorize time in seconds for SPQR
    double SPQR_solve_time ;        // backsolve time in seconds
    double SPQR_flopcount_bound ;   // upper bound on flop count
    double SPQR_tol_used ;          // tolerance used
    double SPQR_norm_E_fro ;        // Frobenius norm of dropped entries

    //--------------------------------------------------------------------------
    // Revised for CHOLMOD v5.0
    //--------------------------------------------------------------------------

    // was size 10 in CHOLMOD v4.2; reduced to 8 in CHOLMOD v5:
    int64_t SPQR_istat [8] ;        // other statistics

    //--------------------------------------------------------------------------
    // Added for CHOLMOD v5.0
    //--------------------------------------------------------------------------

    // These terms have been added to the CHOLMOD Common struct for v5.0, and
    // on most systems they will total 16 bytes.  The preceding term,
    // SPQR_istat, was reduced by 16 bytes, since those last 2 entries were
    // unused in CHOLMOD v4.2.  As a result, the Common struct in v5.0 has the
    // same size as v4.0, and all entries would normally be in the same offset,
    // as well.  This mitigates any changes between v4.0 and v5.0, and may make
    // it easier to upgrade from v4 to v5.

    double nsbounds_hit ;   // # of times diagonal modified by sbound.
                    // This ought to be int64_t, but ndbounds_hit was double in
                    // v4 (see above), so nsbounds_hit is made the same type
                    // for consistency.
    float sbound ;  // Same as dbound,
                    // but for single precision factorization.
    float other_6 ; // for future expansion

    //--------------------------------------------------------------------------
    // GPU configuration and statistics
    //--------------------------------------------------------------------------

    int useGPU ; // 1 if GPU is requested for CHOLMOD
                 // 0 if GPU is not requested for CHOLMOD
                 // -1 if the use of the GPU is in CHOLMOD controled by the
                 // CHOLMOD_USE_GPU environment variable.

    size_t maxGpuMemBytes ;     // GPU control for CHOLMOD
    double maxGpuMemFraction ;  // GPU control for CHOLMOD

    // for SPQR:
    size_t gpuMemorySize ;      // Amount of memory in bytes on the GPU
    double gpuKernelTime ;      // Time taken by GPU kernels
    int64_t gpuFlops ;          // Number of flops performed by the GPU
    int gpuNumKernelLaunches ;  // Number of GPU kernel launches

    #ifdef CHOLMOD_HAS_CUDA
        // these three types are pointers defined by CUDA:
        #define CHOLMOD_CUBLAS_HANDLE cublasHandle_t
        #define CHOLMOD_CUDASTREAM    cudaStream_t
        #define CHOLMOD_CUDAEVENT     cudaEvent_t
    #else
        // they are (void *) if CUDA is not in use:
        #define CHOLMOD_CUBLAS_HANDLE void *
        #define CHOLMOD_CUDASTREAM    void *
        #define CHOLMOD_CUDAEVENT     void *
    #endif

    CHOLMOD_CUBLAS_HANDLE cublasHandle ;

    // a set of streams for general use
    CHOLMOD_CUDASTREAM  gpuStream [CHOLMOD_HOST_SUPERNODE_BUFFERS] ;

    CHOLMOD_CUDAEVENT   cublasEventPotrf [3] ;
    CHOLMOD_CUDAEVENT   updateCKernelsComplete ;
    CHOLMOD_CUDAEVENT   updateCBuffersFree [CHOLMOD_HOST_SUPERNODE_BUFFERS] ;

    void *dev_mempool ; // pointer to single allocation of device memory
    size_t dev_mempool_size ;

    void *host_pinned_mempool ; // pointer to single alloc of pinned mem
    size_t host_pinned_mempool_size ;

    size_t devBuffSize ;
    int    ibuffer ;
    double syrkStart ;          // time syrk started

    // run times of the different parts of CHOLMOD (GPU and CPU):
    double cholmod_cpu_gemm_time ;
    double cholmod_cpu_syrk_time ;
    double cholmod_cpu_trsm_time ;
    double cholmod_cpu_potrf_time ;
    double cholmod_gpu_gemm_time ;
    double cholmod_gpu_syrk_time ;
    double cholmod_gpu_trsm_time ;
    double cholmod_gpu_potrf_time ;
    double cholmod_assemble_time ;
    double cholmod_assemble_time2 ;

    // number of times the BLAS are called on the CPU and the GPU:
    size_t cholmod_cpu_gemm_calls ;
    size_t cholmod_cpu_syrk_calls ;
    size_t cholmod_cpu_trsm_calls ;
    size_t cholmod_cpu_potrf_calls ;
    size_t cholmod_gpu_gemm_calls ;
    size_t cholmod_gpu_syrk_calls ;
    size_t cholmod_gpu_trsm_calls ;
    size_t cholmod_gpu_potrf_calls ;

    double chunk ;      // chunksize for computing # of OpenMP threads to use.
        // Given nwork work to do, # of threads is
        // max (1, min (floor (work / chunk), nthreads_max))

    int nthreads_max ; // max # of OpenMP threads to use in CHOLMOD.
        // Defaults to SUITESPARSE_OPENMP_MAX_THREADS.

    #ifdef BLAS_DUMP
    FILE *blas_dump ;  // only used if CHOLMOD is compiled with -DBLAS_DUMP
    #endif

} cholmod_common ;

// size_t BLAS statistcs in Common:
#define CHOLMOD_CPU_GEMM_CALLS      cholmod_cpu_gemm_calls
#define CHOLMOD_CPU_SYRK_CALLS      cholmod_cpu_syrk_calls
#define CHOLMOD_CPU_TRSM_CALLS      cholmod_cpu_trsm_calls
#define CHOLMOD_CPU_POTRF_CALLS     cholmod_cpu_potrf_calls
#define CHOLMOD_GPU_GEMM_CALLS      cholmod_gpu_gemm_calls
#define CHOLMOD_GPU_SYRK_CALLS      cholmod_gpu_syrk_calls
#define CHOLMOD_GPU_TRSM_CALLS      cholmod_gpu_trsm_calls
#define CHOLMOD_GPU_POTRF_CALLS     cholmod_gpu_potrf_calls

// double BLAS statistics in Common:
#define CHOLMOD_CPU_GEMM_TIME       cholmod_cpu_gemm_time
#define CHOLMOD_CPU_SYRK_TIME       cholmod_cpu_syrk_time
#define CHOLMOD_CPU_TRSM_TIME       cholmod_cpu_trsm_time
#define CHOLMOD_CPU_POTRF_TIME      cholmod_cpu_potrf_time
#define CHOLMOD_GPU_GEMM_TIME       cholmod_gpu_gemm_time
#define CHOLMOD_GPU_SYRK_TIME       cholmod_gpu_syrk_time
#define CHOLMOD_GPU_TRSM_TIME       cholmod_gpu_trsm_time
#define CHOLMOD_GPU_POTRF_TIME      cholmod_gpu_potrf_time
#define CHOLMOD_ASSEMBLE_TIME       cholmod_assemble_time
#define CHOLMOD_ASSEMBLE_TIME2      cholmod_assemble_time2

//------------------------------------------------------------------------------
// cholmod_start:  first call to CHOLMOD
//------------------------------------------------------------------------------

int cholmod_start (cholmod_common *Common) ;
int cholmod_l_start (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_finish:  last call to CHOLMOD
//------------------------------------------------------------------------------

int cholmod_finish (cholmod_common *Common) ;
int cholmod_l_finish (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_defaults: set default parameters
//------------------------------------------------------------------------------

int cholmod_defaults (cholmod_common *Common) ;
int cholmod_l_defaults (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_maxrank:  return valid maximum rank for update/downdate
//------------------------------------------------------------------------------

size_t cholmod_maxrank      // return validated Common->maxrank
(
    // input:
    size_t n,               // # of rows of L and A
    cholmod_common *Common
) ;
size_t cholmod_l_maxrank (size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_allocate_work: allocate workspace in Common
//------------------------------------------------------------------------------

// This method always allocates Xwork as double, for backward compatibility
// with CHOLMOD v4 and earlier.  See cholmod_alloc_work for CHOLMOD v5.

int cholmod_allocate_work
(
    // input:
    size_t nrow,        // size of Common->Flag (nrow int32's)
                        // and Common->Head (nrow+1 int32's)
    size_t iworksize,   // size of Common->Iwork (# of int32's)
    size_t xworksize,   // size of Common->Xwork (# of double's)
    cholmod_common *Common
) ;
int cholmod_l_allocate_work (size_t, size_t, size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_alloc_work: allocate workspace in Common
//------------------------------------------------------------------------------

// Added for CHOLMOD v5: allocates Xwork as either double or single.

int cholmod_alloc_work
(
    // input:
    size_t nrow,        // size of Common->Flag (nrow int32's)
                        // and Common->Head (nrow+1 int32's)
    size_t iworksize,   // size of Common->Iwork (# of int32's)
    size_t xworksize,   // size of Common->Xwork (# of entries)
    int dtype,          // CHOLMOD_DOUBLE or CHOLMOD_SINGLE
    cholmod_common *Common
) ;
int cholmod_l_alloc_work (size_t, size_t, size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_free_work:  free workspace in Common
//------------------------------------------------------------------------------

int cholmod_free_work (cholmod_common *Common) ;
int cholmod_l_free_work (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_clear_flag:  clear Flag workspace in Common
//------------------------------------------------------------------------------

// This macro is deprecated; do not use it:
#define CHOLMOD_CLEAR_FLAG(Common)                      \
{                                                       \
    Common->mark++ ;                                    \
    if (Common->mark <= 0 || Common->mark >= INT32_MAX) \
    {                                                   \
        Common->mark = EMPTY ;                          \
        CHOLMOD (clear_flag) (Common) ;                 \
    }                                                   \
}

int64_t cholmod_clear_flag (cholmod_common *Common) ;
int64_t cholmod_l_clear_flag (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_error:  called when CHOLMOD encounters an error
//------------------------------------------------------------------------------

int cholmod_error
(
    // input:
    int status,             // Common->status
    const char *file,       // source file where error occurred
    int line,               // line number where error occurred
    const char *message,    // error message to print
    cholmod_common *Common
) ;
int cholmod_l_error (int, const char *, int, const char *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_dbound and cholmod_sbound:  for internal use in CHOLMOD only
//------------------------------------------------------------------------------

// These were once documented functions but no are no longer meant to be used
// by the user application.  They remain here for backward compatibility.

double cholmod_dbound   (double, cholmod_common *) ;
double cholmod_l_dbound (double, cholmod_common *) ;
float cholmod_sbound   (float,  cholmod_common *) ;
float cholmod_l_sbound (float,  cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_hypot:  compute sqrt (x*x + y*y) accurately
//------------------------------------------------------------------------------

double cholmod_hypot (double x, double y) ;
double cholmod_l_hypot (double, double) ;

//------------------------------------------------------------------------------
// cholmod_divcomplex:  complex division, c = a/b
//------------------------------------------------------------------------------

int cholmod_divcomplex          // return 1 if divide-by-zero, 0 if OK
(
    // input:
    double ar, double ai,       // a (real, imaginary)
    double br, double bi,       // b (real, imaginary)
    double *cr, double *ci      // c (real, imaginary)
) ;
int cholmod_l_divcomplex (double, double, double, double, double *, double *) ;

//==============================================================================
// cholmod_sparse: a sparse matrix in compressed-column (CSC) form
//==============================================================================

typedef struct cholmod_sparse_struct
{
    size_t nrow ;   // # of rows of the matrix
    size_t ncol ;   // # of colums of the matrix
    size_t nzmax ;  // max # of entries that can be held in the matrix

    // int32_t or int64_t arrays:
    void *p ;   // A->p [0..ncol], column "pointers" of the CSC matrix
    void *i ;   // A->i [0..nzmax-1], the row indices

    // for unpacked matrices only:
    void *nz ;  // A->nz [0..ncol-1], is the # of nonzeros in each col.
        // This is NULL for a "packed" matrix (conventional CSC).
        // For a packed matrix, the jth column is held in A->i and A->x in
        // postions A->p [j] to A->p [j+1]-1, with no gaps between columns.
        // For an "unpacked" matrix, there can be gaps between columns, so
        // the jth columns appears in positions A-p [j] to
        // A->p [j] + A->nz [j] - 1.

    // double or float arrays:
    void *x ;   // size nzmax or 2*nzmax, or NULL
    void *z ;   // size nzmax, or NULL

    int stype ; // A->stype defines what parts of the matrix is held:
        // 0:  the matrix is unsymmetric with both lower and upper parts stored.
        // >0: the matrix is square and symmetric, with just the upper
        //     triangular part stored.
        // <0: the matrix is square and symmetric, with just the lower
        //     triangular part stored.

    int itype ; // A->itype defines the integers used for A->p, A->i, and A->nz.
        // if CHOLMOD_INT, these arrays are all of type int32_t.
        // if CHOLMOD_LONG, these arrays are all of type int64_t.
    int xtype ;     // pattern, real, complex, or zomplex
    int dtype ;     // x and z are double or single
    int sorted ;    // true if columns are sorted, false otherwise
    int packed ;    // true if packed (A->nz ignored), false if unpacked

} cholmod_sparse ;

//------------------------------------------------------------------------------
// cholmod_allocate_sparse:  allocate a sparse matrix
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_allocate_sparse
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    size_t nzmax,   // max # of entries the matrix can hold
    int sorted,     // true if columns are sorted
    int packed,     // true if A is be packed (A->nz NULL), false if unpacked
    int stype,      // the stype of the matrix (unsym, tril, or triu)
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_allocate_sparse (size_t, size_t, size_t, int, int,
    int, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_free_sparse:  free a sparse matrix
//------------------------------------------------------------------------------

int cholmod_free_sparse
(
    // input/output:
    cholmod_sparse **A,         // handle of sparse matrix to free
    cholmod_common *Common
) ;
int cholmod_l_free_sparse (cholmod_sparse **, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_reallocate_sparse: change max # of entries in a sparse matrix
//------------------------------------------------------------------------------

int cholmod_reallocate_sparse
(
    // input:
    size_t nznew,       // new max # of nonzeros the sparse matrix can hold
    // input/output:
    cholmod_sparse *A,  // sparse matrix to reallocate
    cholmod_common *Common
) ;
int cholmod_l_reallocate_sparse (size_t, cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_nnz: # of entries in a sparse matrix
//------------------------------------------------------------------------------

int64_t cholmod_nnz             // return # of entries in the sparse matrix
(
    // input:
    cholmod_sparse *A,          // sparse matrix to query
    cholmod_common *Common
) ;
int64_t cholmod_l_nnz (cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_speye:  sparse identity matrix (possibly rectangular)
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_speye
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_speye (size_t, size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_spzeros: sparse matrix with no entries
//------------------------------------------------------------------------------

// Identical to cholmod_allocate_sparse, with packed = true, sorted = true,
// and stype = 0.

cholmod_sparse *cholmod_spzeros     // return a sparse matrix with no entries
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    size_t nzmax,   // max # of entries the matrix can hold
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_spzeros (size_t, size_t, size_t, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_transpose: transpose a sparse matrix
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_transpose       // return new sparse matrix C
(
    // input:
    cholmod_sparse *A,  // input matrix
    int mode,           // 2: numerical (conj)
                        // 1: numerical (non-conj.)
                        // 0: pattern (with diag)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_transpose (cholmod_sparse *, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_transpose_unsym:  transpose an unsymmetric sparse matrix
//------------------------------------------------------------------------------

// Compute C = A', A (:,f)', or A (p,f)', where A is unsymmetric and C is
// already allocated.  See cholmod_transpose for a routine with a simpler
// interface.

int cholmod_transpose_unsym
(
    // input:
    cholmod_sparse *A,  // input matrix
    int mode,           // 2: numerical (conj)
                        // 1: numerical (non-conj.),
                        // 0: pattern (with diag)
    int32_t *Perm,      // permutation for C=A(p,f)', or NULL
    int32_t *fset,      // a list of column indices in range 0:A->ncol-1
    size_t fsize,       // # of entries in fset
    // input/output:
    cholmod_sparse *C,  // output matrix, must be allocated on input
    cholmod_common *Common
) ;
int cholmod_l_transpose_unsym (cholmod_sparse *, int, int64_t *, int64_t *,
    size_t, cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_transpose_sym:  symmetric permuted transpose
//------------------------------------------------------------------------------

// C = A' or C = A(p,p)' where A and C are both symmetric and C is already
// allocated.  See cholmod_transpose or cholmod_ptranspose for a routine with
// a simpler interface.

int cholmod_transpose_sym
(
    // input:
    cholmod_sparse *A,  // input matrix
    int mode,           // 2: numerical (conj)
                        // 1: numerical (non-conj.),
                        // 0: pattern (with diag)
    int32_t *Perm,      // permutation for C=A(p,p)', or NULL
    // input/output:
    cholmod_sparse *C,  // output matrix, must be allocated on input
    cholmod_common *Common
) ;
int cholmod_l_transpose_sym (cholmod_sparse *, int, int64_t *, cholmod_sparse *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_ptranspose: C = A', A(:,f)', A(p,p)', or A(p,f)'
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_ptranspose      // return new sparse matrix C
(
    // input:
    cholmod_sparse *A,  // input matrix
    int mode,           // 2: numerical (conj)
                        // 1: numerical (non-conj.)
                        // 0: pattern (with diag)
    int32_t *Perm,      // permutation for C=A(p,f)', or NULL
    int32_t *fset,      // a list of column indices in range 0:A->ncol-1
    size_t fsize,       // # of entries in fset
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_ptranspose (cholmod_sparse *, int, int64_t *,
    int64_t *, size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_sort: sort the indices of a sparse matrix
//------------------------------------------------------------------------------

int cholmod_sort
(
    // input/output:
    cholmod_sparse *A,      // input/output matrix to sort
    cholmod_common *Common
) ;
int cholmod_l_sort (cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_band_nnz: # of entries within a band of a sparse matrix
//------------------------------------------------------------------------------

int64_t cholmod_band_nnz    // return # of entries in a band (-1 if error)
(
    // input:
    cholmod_sparse *A,      // matrix to examine
    int64_t k1,             // count entries in k1:k2 diagonals
    int64_t k2,
    bool ignore_diag,       // if true, exclude any diagonal entries
    cholmod_common *Common
) ;
int64_t cholmod_l_band_nnz (cholmod_sparse *, int64_t, int64_t, bool,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_band:  C = tril (triu (A,k1), k2)
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_band    // return a new matrix C
(
    // input:
    cholmod_sparse *A,      // input matrix
    int64_t k1,             // count entries in k1:k2 diagonals
    int64_t k2,
    int mode,               // >0: numerical, 0: pattern, <0: pattern (no diag)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_band (cholmod_sparse *, int64_t, int64_t, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_band_inplace:  A = tril (triu (A,k1), k2)
//------------------------------------------------------------------------------

int cholmod_band_inplace
(
    // input:
    int64_t k1,             // count entries in k1:k2 diagonals
    int64_t k2,
    int mode,               // >0: numerical, 0: pattern, <0: pattern (no diag)
    // input/output:
    cholmod_sparse *A,      // input/output matrix
    cholmod_common *Common
) ;
int cholmod_l_band_inplace (int64_t, int64_t, int, cholmod_sparse *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_aat: C = A*A' or A(:,f)*A(:,f)'
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_aat     // return sparse matrix C
(
    // input:
    cholmod_sparse *A,  // input matrix
    int32_t *fset,      // a list of column indices in range 0:A->ncol-1
    size_t fsize,       // # of entries in fset
    int mode,           // 2: numerical (conj)
                        // 1: numerical (non-conj.),
                        // 0: pattern (with diag)
                        // -1: pattern (remove diag),
                        // -2: pattern (remove diag; add ~50% extra space in C)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_aat (cholmod_sparse *, int64_t *, size_t, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_copy_sparse:  C = A, create an exact copy of a sparse matrix
//------------------------------------------------------------------------------

// Creates an exact copy of a sparse matrix.  For making a copy with a change
// of stype and/or copying the pattern of a numerical matrix, see cholmod_copy.
// For changing the xtype and/or dtype, see cholmod_sparse_xtype.

cholmod_sparse *cholmod_copy_sparse  // return new sparse matrix
(
    // input:
    cholmod_sparse *A,     // sparse matrix to copy
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_copy_sparse (cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_copy:  C = A, with possible change of stype
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_copy        // return new sparse matrix
(
    // input:
    cholmod_sparse *A,  // input matrix, not modified
    int stype,          // stype of C
    int mode,           // 2: numerical (conj)
                        // 1: numerical (non-conj.)
                        // 0: pattern (with diag)
                        // -1: pattern (remove diag)
                        // -2: pattern (remove diag; add ~50% extra space in C)
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_copy (cholmod_sparse *, int, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_add: C = alpha*A + beta*B
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_add     // return C = alpha*A + beta*B
(
    // input:
    cholmod_sparse *A,  // input matrix
    cholmod_sparse *B,  // input matrix
    double alpha [2],   // scale factor for A (two entires used if complex)
    double beta [2],    // scale factor for A (two entires used if complex)
    int mode,           // 2: numerical (conj) if A and/or B are symmetric,
                        // 1: numerical (non-conj.) if A and/or B are symmetric.
                        // 0: pattern
    int sorted,         // ignored; C is now always returned as sorted
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_add (cholmod_sparse *, cholmod_sparse *, double [2],
    double [2], int, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_sparse_xtype: change the xtype and/or dtype of a sparse matrix
//------------------------------------------------------------------------------

int cholmod_sparse_xtype
(
    // input:
    int to_xdtype,      // requested xtype and dtype
    // input/output:
    cholmod_sparse *A,  // sparse matrix to change
    cholmod_common *Common
) ;
int cholmod_l_sparse_xtype (int, cholmod_sparse *, cholmod_common *) ;

//==============================================================================
// cholmod_factor: symbolic or numeric factorization (simplicial or supernodal)
//==============================================================================

typedef struct cholmod_factor_struct
{
    size_t n ;      // L is n-by-n

    size_t minor ;  // If the factorization failed because of numerical issues
        // (the matrix being factorized is found to be singular or not positive
        // definte), then L->minor is the column at which it failed.  L->minor
        // = n means the factorization was successful.

    //--------------------------------------------------------------------------
    // symbolic ordering and analysis
    //--------------------------------------------------------------------------

    void *Perm ;    // int32/int64, size n, fill-reducing ordering
    void *ColCount ;// int32/int64, size n, # entries in each column of L
    void *IPerm ;   // int32/int64, size n, created by cholmod_solve2;
                    // containing the inverse of L->Perm

    //--------------------------------------------------------------------------
    // simplicial factorization (not supernodal)
    //--------------------------------------------------------------------------

    // The row indices of L(:,j) are held in L->i [L->p [j] ... L->p [j] +
    // L->nz [j] - 1].  The numeical values of L(:,j) are held in the same
    // positions in L->x (and L->z if L is zomplex).  L->next and L->prev hold
    // a link list of columns of L, that tracks the order they appear in the
    // arrays L->i, L->x, and L->z.  The head and tail of the list is n+1 and
    // n, respectively.

    size_t nzmax ;  // # of entries that L->i, L->x, and L->z can hold
    void *p ;       // int32/int64, size n+1, column pointers
    void *i ;       // int32/int64, size nzmax, row indices
    void *x ;       // float/double, size nzmax or 2*nzmax, numerical values
    void *z ;       // float/double, size nzmax or empty, imaginary values
    void *nz ;      // int32/int64, size ncol, # of entries in each column
    void *next ;    // int32/int64, size n+2
    void *prev ;    // int32/int64, size n+2

    //--------------------------------------------------------------------------
    // supernodal factorization (not simplicial)
    //--------------------------------------------------------------------------

    // L->x is shared with the simplicial structure above.  L->z is not used
    // for the supernodal case since a supernodal factor cannot be zomplex.

    size_t nsuper ;     // # of supernodes
    size_t ssize ;      // # of integers in L->s
    size_t xsize ;      // # of entries in L->x
    size_t maxcsize ;   // size of largest update matrix
    size_t maxesize ;   // max # of rows in supernodes, excl. triangular part
    // the following are int32/int64 and are size nsuper+1:
    void *super ;       // first column in each supernode
    void *pi ;          // index into L->s for integer part of a supernode
    void *px ;          // index into L->x for numeric part of a supernode
    // int32/int64, of size ssize:
    void *s ;           // integer part of supernodes

    //--------------------------------------------------------------------------
    // type of the factorization
    //--------------------------------------------------------------------------

    int ordering ;      // the fill-reducing method used (CHOLMOD_NATURAL,
        // CHOLMOD_GIVEN, CHOLMOD_AMD, CHOLMOD_METIS, CHOLMOD_NESDIS,
        // CHOLMOD_COLAMD, or CHOLMOD_POSTORDERED).

    int is_ll ;         // true: an LL' factorization; false: LDL' instead
    int is_super ;      // true: supernodal; false: simplicial
    int is_monotonic ;  // true: columns appear in order 0 to n-1 in L, for a
                        // simplicial factorization only

    // Two boolean values above (is_ll, is_super) and L->xtype (pattern or
    // otherwise, define eight types of factorizations, but only 6 are used:

    // If L->xtype is CHOLMOD_PATTERN, then L is a symbolic factor:
    //
    // simplicial LDL': (is_ll false, is_super false).  Nothing is present
    //      except Perm and ColCount.
    //
    // simplicial LL': (is_ll true, is_super false).  Identical to the
    //      simplicial LDL', except for the is_ll flag.
    //
    // supernodal LL': (is_ll true, is_super true).  A supernodal symbolic
    //      factorization.  The simplicial symbolic information is present
    //      (Perm and ColCount), as is all of the supernodal factorization
    //      except for the numerical values (x and z).
    //
    // If L->xtype is CHOLMOD_REAL, CHOLMOD_COMPLEX, or CHOLMOD_ZOMPLEX,
    // then L is a numeric factor:
    //
    // simplicial LDL':  (is_ll false, is_super false).  Stored in compressed
    //      column form, using the simplicial components above (nzmax, p, i,
    //      x, z, nz, next, and prev).  The unit diagonal of L is not stored,
    //      and D is stored in its place.  There are no supernodes.
    //
    // simplicial LL': (is_ll true, is_super false).  Uses the same storage
    //      scheme as the simplicial LDL', except that D does not appear.
    //      The first entry of each column of L is the diagonal entry of
    //      that column of L.
    //
    // supernodal LL': (is_ll true, is_super true).  A supernodal factor,
    //      using the supernodal components described above (nsuper, ssize,
    //      xsize, maxcsize, maxesize, super, pi, px, s, x, and z).
    //      A supernodal factorization is never zomplex.

    int itype ; // integer type for L->Perm, L->ColCount, L->p, L->i, L->nz,
                // L->next, L->prev, L->super, L->pi, L->px, and L->s.
                // These are all int32 if L->itype is CHOLMOD_INT, or all int64
                // if L->itype is CHOLMOD_LONG.

    int xtype ; // pattern, real, complex, or zomplex
    int dtype ; // x and z are double or single

    int useGPU; // if true, symbolic factorization allows for use of the GPU

} cholmod_factor ;

//------------------------------------------------------------------------------
// cholmod_allocate_factor: allocate a numerical factor
//------------------------------------------------------------------------------

// L is returned as double precision

cholmod_factor *cholmod_allocate_factor         // return the new factor L
(
    // input:
    size_t n,               // L is factorization of an n-by-n matrix
    cholmod_common *Common
) ;
cholmod_factor *cholmod_l_allocate_factor (size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_alloc_factor: allocate a numerical factor (double or single)
//------------------------------------------------------------------------------

cholmod_factor *cholmod_alloc_factor    // return the new factor L
(
    // input:
    size_t n,               // L is factorization of an n-by-n matrix
    int dtype,              // CHOLMOD_SINGLE or CHOLMOD_DOUBLE
    cholmod_common *Common
) ;
cholmod_factor *cholmod_l_alloc_factor (size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_free_factor:  free a factor
//------------------------------------------------------------------------------

int cholmod_free_factor
(
    // input/output:
    cholmod_factor **L,         // handle of sparse factorization to free
    cholmod_common *Common
) ;
int cholmod_l_free_factor (cholmod_factor **, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_reallocate_factor:  change the # entries in a factor
//------------------------------------------------------------------------------

int cholmod_reallocate_factor
(
    // input:
    size_t nznew,       // new max # of nonzeros the factor matrix can hold
    // input/output:
    cholmod_factor *L,  // factor to reallocate
    cholmod_common *Common
) ;
int cholmod_l_reallocate_factor (size_t, cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_change_factor:  change the type of factor (e.g., LDL' to LL')
//------------------------------------------------------------------------------

int cholmod_change_factor
(
    // input:
    int to_xtype,       // CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX;
                        // L->dtype remains unchanged.
    int to_ll,          // if true: convert to LL'; else to LDL'
    int to_super,       // if true: convert to supernodal; else to simplicial
    int to_packed,      // if true: pack simplicial columns; else: do not pack
    int to_monotonic,   // if true, put simplicial columns in order
    // input/output:
    cholmod_factor *L,  // factor to change.
    cholmod_common *Common
) ;
int cholmod_l_change_factor (int, int, int, int, int, cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_pack_factor:  pack a factor
//------------------------------------------------------------------------------

// Removes all slack space from all columns in a factor.

int cholmod_pack_factor
(
    // input/output:
    cholmod_factor *L,      // factor to pack
    cholmod_common *Common
) ;
int cholmod_l_pack_factor (cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_reallocate_column:  reallocate a single column L(:,j)
//------------------------------------------------------------------------------

int cholmod_reallocate_column
(
    // input:
    size_t j,                   // reallocate L(:,j)
    size_t need,                // space in L(:,j) for this # of entries
    // input/output:
    cholmod_factor *L,          // L factor modified, L(:,j) resized
    cholmod_common *Common
) ;
int cholmod_l_reallocate_column (size_t, size_t, cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_factor_to_sparse:  create a sparse matrix copy of a factor
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_factor_to_sparse    // return a new sparse matrix
(
    // input/output:
    cholmod_factor *L,  // input: factor to convert; output: L is converted
                        // to a simplicial symbolic factor
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_factor_to_sparse (cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_copy_factor:  create a copy of a factor
//------------------------------------------------------------------------------

cholmod_factor *cholmod_copy_factor     // return a copy of the factor
(
    // input:
    cholmod_factor *L,      // factor to copy (not modified)
    cholmod_common *Common
) ;
cholmod_factor *cholmod_l_copy_factor (cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_factor_xtype: change the xtype and/or dtype of a factor
//------------------------------------------------------------------------------

int cholmod_factor_xtype
(
    // input:
    int to_xdtype,      // requested xtype and dtype
    // input/output:
    cholmod_factor *L,  // factor to change
    cholmod_common *Common
) ;
int cholmod_l_factor_xtype (int, cholmod_factor *, cholmod_common *) ;

//==============================================================================
// cholmod_dense: a dense matrix, held by column
//==============================================================================

typedef struct cholmod_dense_struct
{
    size_t nrow ;       // the matrix is nrow-by-ncol
    size_t ncol ;
    size_t nzmax ;      // maximum number of entries in the matrix
    size_t d ;          // leading dimension (d >= nrow must hold)
    void *x ;           // size nzmax or 2*nzmax, if present
    void *z ;           // size nzmax, if present
    int xtype ;         // pattern, real, complex, or zomplex
    int dtype ;         // x and z double or single

} cholmod_dense ;

//------------------------------------------------------------------------------
// cholmod_allocate_dense: allocate a dense matrix (contents not initialized)
//------------------------------------------------------------------------------

cholmod_dense *cholmod_allocate_dense
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    size_t d,       // leading dimension
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_allocate_dense (size_t, size_t, size_t, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_zeros: allocate a dense matrix and set it to zero
//------------------------------------------------------------------------------

cholmod_dense *cholmod_zeros
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_zeros (size_t, size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_ones: allocate a dense matrix of all 1's
//------------------------------------------------------------------------------

cholmod_dense *cholmod_ones
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (_REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_ones (size_t, size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_eye: allocate a dense identity matrix
//------------------------------------------------------------------------------

cholmod_dense *cholmod_eye      // return a dense identity matrix
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (_REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_eye (size_t, size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_free_dense:  free a dense matrix
//------------------------------------------------------------------------------

int cholmod_free_dense
(
    // input/output:
    cholmod_dense **X,          // handle of dense matrix to free
    cholmod_common *Common
) ;
int cholmod_l_free_dense (cholmod_dense **, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_ensure_dense:  ensure a dense matrix has a given size and type
//------------------------------------------------------------------------------

cholmod_dense *cholmod_ensure_dense
(
    // input/output:
    cholmod_dense **X,  // matrix to resize as needed (*X may be NULL)
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    size_t d,       // leading dimension
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_ensure_dense (cholmod_dense **, size_t, size_t,
    size_t, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_sparse_to_dense:  create a dense matrix copy of a sparse matrix
//------------------------------------------------------------------------------

cholmod_dense *cholmod_sparse_to_dense      // return a dense matrix
(
    // input:
    cholmod_sparse *A,      // input matrix
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_sparse_to_dense (cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_dense_nnz: count # of nonzeros in a dense matrix
//------------------------------------------------------------------------------

int64_t cholmod_dense_nnz       // return # of entries in the dense matrix
(
    // input:
    cholmod_dense *X,       // input matrix
    cholmod_common *Common
) ;
int64_t cholmod_l_dense_nnz (cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_dense_to_sparse:  create a sparse matrix copy of a dense matrix
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_dense_to_sparse         // return a sparse matrix C
(
    // input:
    cholmod_dense *X,       // input matrix
    int mode,               // 1: copy the values
                            // 0: C is pattern
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_dense_to_sparse (cholmod_dense *, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_copy_dense:  create a copy of a dense matrix
//------------------------------------------------------------------------------

cholmod_dense *cholmod_copy_dense   // returns new dense matrix
(
    // input:
    cholmod_dense *X,   // input dense matrix
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_copy_dense (cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_copy_dense2:  copy a dense matrix (pre-allocated)
//------------------------------------------------------------------------------

int cholmod_copy_dense2
(
    // input:
    cholmod_dense *X,   // input dense matrix
    // input/output:
    cholmod_dense *Y,   // output dense matrix (already allocated on input)
    cholmod_common *Common
) ;
int cholmod_l_copy_dense2 (cholmod_dense *, cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_dense_xtype: change the xtype and/or dtype of a dense matrix
//------------------------------------------------------------------------------

int cholmod_dense_xtype
(
    // input:
    int to_xdtype,      // requested xtype and dtype
    // input/output:
    cholmod_dense *X,   // dense matrix to change
    cholmod_common *Common
) ;
int cholmod_l_dense_xtype (int, cholmod_dense *, cholmod_common *) ;

//=============================================================================
// cholmod_triplet: a sparse matrix in triplet form
//=============================================================================

typedef struct cholmod_triplet_struct
{
    size_t nrow ;   // # of rows of the matrix
    size_t ncol ;   // # of colums of the matrix
    size_t nzmax ;  // max # of entries that can be held in the matrix
    size_t nnz ;    // current # of entries can be held in the matrix

    // int32 or int64 arrays (depending on T->itype)
    void *i ;   // i [0..nzmax-1], the row indices
    void *j ;   // j [0..nzmax-1], the column indices

    // double or float arrays:
    void *x ;   // size nzmax or 2*nzmax, or NULL
    void *z ;   // size nzmax, or NULL

    int stype ; // T->stype defines what parts of the matrix is held:
        // 0:  the matrix is unsymmetric with both lower and upper parts stored.
        // >0: the matrix is square and symmetric, where entries in the lower
        //      triangular part are transposed and placed in the upper
        //      triangular part of A if T is converted into a sparse matrix A.
        // <0: the matrix is square and symmetric, where entries in the upper
        //      triangular part are transposed and placed in the lower
        //      triangular part of A if T is converted into a sparse matrix A.
        //
        // Note that A->stype (for a sparse matrix) and T->stype (for a
        // triplet matrix) are handled differently.  In a triplet matrix T,
        // no entry is ever ignored.  For a sparse matrix A, if A->stype < 0
        // or A->stype > 0, then entries not in the correct triangular part
        // are ignored.

    int itype ; // T->itype defines the integers used for T->i and T->j.
        // if CHOLMOD_INT, these arrays are all of type int32_t.
        // if CHOLMOD_LONG, these arrays are all of type int64_t.
    int xtype ;     // pattern, real, complex, or zomplex
    int dtype ;     // x and z are double or single

} cholmod_triplet ;

//------------------------------------------------------------------------------
// cholmod_allocate_triplet: allocate a triplet matrix
//------------------------------------------------------------------------------

cholmod_triplet *cholmod_allocate_triplet       // return triplet matrix T
(
    // input:
    size_t nrow,    // # of rows
    size_t ncol,    // # of columns
    size_t nzmax,   // max # of entries the matrix can hold
    int stype,      // the stype of the matrix (unsym, tril, or triu)
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX)
    cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_allocate_triplet (size_t, size_t, size_t, int, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_free_triplet: free a triplet matrix
//------------------------------------------------------------------------------

int cholmod_free_triplet
(
    // input/output:
    cholmod_triplet **T,        // handle of triplet matrix to free
    cholmod_common *Common
) ;
int cholmod_l_free_triplet (cholmod_triplet **, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_reallocate_triplet: change max # of entries in a triplet matrix
//------------------------------------------------------------------------------

int cholmod_reallocate_triplet
(
    // input:
    size_t nznew,       // new max # of nonzeros the triplet matrix can hold
    // input/output:
    cholmod_triplet *T, // triplet matrix to reallocate
    cholmod_common *Common
) ;
int cholmod_l_reallocate_triplet (size_t, cholmod_triplet *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_sparse_to_triplet:  create a triplet matrix copy of a sparse matrix
//------------------------------------------------------------------------------

cholmod_triplet *cholmod_sparse_to_triplet
(
    // input:
    cholmod_sparse *A,      // matrix to copy into triplet form T
    cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_sparse_to_triplet (cholmod_sparse *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_triplet_to_sparse: create a sparse matrix from of triplet matrix
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_triplet_to_sparse       // return sparse matrix A
(
    // input:
    cholmod_triplet *T,     // input triplet matrix
    size_t nzmax,           // allocate space for max(nzmax,nnz(A)) entries
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_triplet_to_sparse (cholmod_triplet *, size_t,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_copy_triplet: copy a triplet matrix
//------------------------------------------------------------------------------

cholmod_triplet *cholmod_copy_triplet   // return new triplet matrix
(
    // input:
    cholmod_triplet *T,     // triplet matrix to copy
    cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_copy_triplet (cholmod_triplet *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_triplet_xtype: change the xtype and/or dtype of a triplet matrix
//------------------------------------------------------------------------------

int cholmod_triplet_xtype
(
    // input:
    int to_xdtype,      // requested xtype and dtype
    // input/output:
    cholmod_triplet *T, // triplet matrix to change
    cholmod_common *Common
) ;
int cholmod_l_triplet_xtype (int, cholmod_triplet *, cholmod_common *) ;

//------------------------------------------------------------------------------
// memory allocation: malloc/calloc/realloc/free
//------------------------------------------------------------------------------

// These methods act like malloc/calloc/realloc/free, with some differences.
// They are simple wrappers around the memory management functions in
// SuiteSparse_config.  cholmod_malloc and cholmod_calloc have the same
// signature, unlike malloc and calloc.  If cholmod_free is given a NULL
// pointer, it safely does nothing.  cholmod_free must be passed the size of
// the object being freed, but that is just to keep track of memory usage
// statistics. cholmod_realloc does not return NULL if it fails; instead, it
// returns the pointer to the unmodified block of memory.

void *cholmod_malloc    // return pointer to newly allocated memory
(
    // input:
    size_t n,           // number of items
    size_t size,        // size of each item
    cholmod_common *Common
) ;
void *cholmod_l_malloc (size_t, size_t, cholmod_common *) ;

void *cholmod_calloc    // return pointer to newly allocated memory
(
    // input:
    size_t n,           // number of items
    size_t size,        // size of each item
    cholmod_common *Common
) ;
void *cholmod_l_calloc (size_t, size_t, cholmod_common *) ;

void *cholmod_free      // returns NULL to simplify its usage
(
    // input:
    size_t n,           // number of items
    size_t size,        // size of each item
    // input/output:
    void *p,            // memory to free
    cholmod_common *Common
) ;
void *cholmod_l_free (size_t, size_t, void *, cholmod_common *) ;

void *cholmod_realloc   // return newly reallocated block of memory
(
    // input:
    size_t nnew,        // # of items in newly reallocate memory
    size_t size,        // size of each item
    // input/output:
    void *p,            // pointer to memory to reallocate (may be NULL)
    size_t *n,          // # of items in p on input; nnew on output if success
    cholmod_common *Common
) ;
void *cholmod_l_realloc (size_t, size_t, void *, size_t *, cholmod_common *) ;

int cholmod_realloc_multiple    // returns true if successful, false otherwise
(
    // input:
    size_t nnew,    // # of items in newly reallocate memory
    int nint,       // 0: do not allocate I_block or J_block, 1: just I_block,
                    // 2: both I_block and J_block
    int xdtype,     // xtype + dtype of the matrix:
                    // (CHOLMOD_DOUBLE, _SINGLE) +
                    // (CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX)
    // input/output:
    void **I_block,       // integer block of memory (int32_t or int64_t)
    void **J_block,       // integer block of memory (int32_t or int64_t)
    void **X_block,       // real or complex, double or single, block
    void **Z_block,       // zomplex only: double or single block
    size_t *n,      // current size of I_block, J_block, X_block, and/or Z_block
                    // on input,  changed to nnew on output, if successful
    cholmod_common *Common
) ;
int cholmod_l_realloc_multiple (size_t, int, int, void **, void **, void **,
    void **, size_t *, cholmod_common *) ;

//------------------------------------------------------------------------------
// numerical comparisons
//------------------------------------------------------------------------------

// These macros were different on Windows for older versions of CHOLMOD.
// They are no longer needed but are kept for backward compatibility.

#define CHOLMOD_IS_NAN(x)       isnan (x)
#define CHOLMOD_IS_ZERO(x)      ((x) == 0.)
#define CHOLMOD_IS_NONZERO(x)   ((x) != 0.)
#define CHOLMOD_IS_LT_ZERO(x)   ((x) < 0.)
#define CHOLMOD_IS_GT_ZERO(x)   ((x) > 0.)
#define CHOLMOD_IS_LE_ZERO(x)   ((x) <= 0.)

#endif

//==============================================================================
// CHOLMOD:Check Module
//==============================================================================

#ifndef NCHECK

// Routines that check and print the 5 basic data types in CHOLMOD, and 3 kinds
// of integer vectors (subset, perm, and parent), and read in matrices from a
// file:
//
// cholmod_check_common     check/print the Common object
// cholmod_print_common
//
// cholmod_check_sparse     check/print a sparse matrix in column-oriented form
// cholmod_print_sparse
//
// cholmod_check_dense      check/print a dense matrix
// cholmod_print_dense
//
// cholmod_check_factor     check/print a Cholesky factorization
// cholmod_print_factor
//
// cholmod_check_triplet    check/print a sparse matrix in triplet form
// cholmod_print_triplet
//
// cholmod_check_subset     check/print a subset (integer vector in given range)
// cholmod_print_subset
//
// cholmod_check_perm       check/print a permutation (an integer vector)
// cholmod_print_perm
//
// cholmod_check_parent     check/print an elimination tree (an integer vector)
// cholmod_print_parent
//
// cholmod_read_triplet     read a matrix in triplet form (any Matrix Market
//                          "coordinate" format, or a generic triplet format).
//
// cholmod_read_sparse      read a matrix in sparse form (same file format as
//                          cholmod_read_triplet).
//
// cholmod_read_dense       read a dense matrix (any Matrix Market "array"
//                          format, or a generic dense format).
//
// cholmod_write_sparse     write a sparse matrix to a Matrix Market file.
//
// cholmod_write_dense      write a dense matrix to a Matrix Market file.
//
// cholmod_print_common and cholmod_check_common are the only two routines that
// you may call after calling cholmod_finish.
//
// Requires the Utility module.  Not required by any CHOLMOD module, except when
// debugging is enabled (in which case all modules require the Check module).
//
// See cholmod_read.c for a description of the file formats supported by the
// cholmod_read_* routines.

//------------------------------------------------------------------------------
// cholmod_check_common:  check the Common object
//------------------------------------------------------------------------------

int cholmod_check_common
(
    cholmod_common *Common
) ;
int cholmod_l_check_common (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_common:  print the Common object
//------------------------------------------------------------------------------

int cholmod_print_common
(
    // input:
    const char *name,   // printed name of Common object
    cholmod_common *Common
) ;

int cholmod_l_print_common (const char *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_gpu_stats:  print the GPU / CPU statistics
//------------------------------------------------------------------------------

int cholmod_gpu_stats   (cholmod_common *) ;
int cholmod_l_gpu_stats (cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_sparse:  check a sparse matrix
//------------------------------------------------------------------------------

int cholmod_check_sparse
(
    // input:
    cholmod_sparse *A,  // sparse matrix to check
    cholmod_common *Common
) ;
int cholmod_l_check_sparse (cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_sparse
//------------------------------------------------------------------------------

int cholmod_print_sparse
(
    // input:
    cholmod_sparse *A,  // sparse matrix to print
    const char *name,   // printed name of sparse matrix
    cholmod_common *Common
) ;
int cholmod_l_print_sparse (cholmod_sparse *, const char *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_dense:  check a dense matrix
//------------------------------------------------------------------------------

int cholmod_check_dense
(
    // input:
    cholmod_dense *X,   // dense matrix to check
    cholmod_common *Common
) ;
int cholmod_l_check_dense (cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_dense:  print a dense matrix
//------------------------------------------------------------------------------

int cholmod_print_dense
(
    // input:
    cholmod_dense *X,   // dense matrix to print
    const char *name,   // printed name of dense matrix
    cholmod_common *Common
) ;
int cholmod_l_print_dense (cholmod_dense *, const char *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_factor:  check a factor
//------------------------------------------------------------------------------

int cholmod_check_factor
(
    // input:
    cholmod_factor *L,  // factor to check
    cholmod_common *Common
) ;
int cholmod_l_check_factor (cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_factor:  print a factor
//------------------------------------------------------------------------------

int cholmod_print_factor
(
    // input:
    cholmod_factor *L,  // factor to print
    const char *name,   // printed name of factor
    cholmod_common *Common
) ;
int cholmod_l_print_factor (cholmod_factor *, const char *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_triplet:  check a sparse matrix in triplet form
//------------------------------------------------------------------------------

int cholmod_check_triplet
(
    // input:
    cholmod_triplet *T, // triplet matrix to check
    cholmod_common *Common
) ;
int cholmod_l_check_triplet (cholmod_triplet *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_triplet:  print a triplet matrix
//------------------------------------------------------------------------------

int cholmod_print_triplet
(
    // input:
    cholmod_triplet *T, // triplet matrix to print
    const char *name,   // printed name of triplet matrix
    cholmod_common *Common
) ;
int cholmod_l_print_triplet (cholmod_triplet *, const char *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_subset:  check a subset
//------------------------------------------------------------------------------

int cholmod_check_subset
(
    // input:
    int32_t *Set,       // Set [0:len-1] is a subset of 0:n-1.  Duplicates OK
    int64_t len,        // size of Set (an integer array)
    size_t n,           // 0:n-1 is valid range
    cholmod_common *Common
) ;
int cholmod_l_check_subset (int64_t *, int64_t, size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_subset:  print a subset
//------------------------------------------------------------------------------

int cholmod_print_subset
(
    // input:
    int32_t *Set,       // Set [0:len-1] is a subset of 0:n-1.  Duplicates OK
    int64_t len,        // size of Set (an integer array)
    size_t n,           // 0:n-1 is valid range
    const char *name,   // printed name of Set
    cholmod_common *Common
) ;
int cholmod_l_print_subset (int64_t *, int64_t, size_t, const char *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_perm:  check a permutation
//------------------------------------------------------------------------------

int cholmod_check_perm
(
    // input:
    int32_t *Perm,      // Perm [0:len-1] is a permutation of subset of 0:n-1
    size_t len,         // size of Perm (an integer array)
    size_t n,           // 0:n-1 is valid range
    cholmod_common *Common
) ;
int cholmod_l_check_perm (int64_t *, size_t, size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_perm:  print a permutation vector
//------------------------------------------------------------------------------

int cholmod_print_perm
(
    // input:
    int32_t *Perm,      // Perm [0:len-1] is a permutation of subset of 0:n-1
    size_t len,         // size of Perm (an integer array)
    size_t n,           // 0:n-1 is valid range
    const char *name,   // printed name of Perm
    cholmod_common *Common
) ;
int cholmod_l_print_perm (int64_t *, size_t, size_t, const char *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_check_parent:  check an elimination tree
//------------------------------------------------------------------------------

int cholmod_check_parent
(
    // input:
    int32_t *Parent,    // Parent [0:n-1] is an elimination tree
    size_t n,           // size of Parent
    cholmod_common *Common
) ;
int cholmod_l_check_parent (int64_t *, size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_print_parent
//------------------------------------------------------------------------------

int cholmod_print_parent
(
    // input:
    int32_t *Parent,    // Parent [0:n-1] is an elimination tree
    size_t n,           // size of Parent
    const char *name,   // printed name of Parent
    cholmod_common *Common
) ;
int cholmod_l_print_parent (int64_t *, size_t, const char *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_sparse: read a sparse matrix from a file (double only)
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_read_sparse     // return sparse matrix (double)
(
    // input:
    FILE *f,        // file to read from, must already be open
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_read_sparse (FILE *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_sparse2: read a sparse matrix from a file (float or double)
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_read_sparse2    // return sparse matrix (double/single)
(
    // input:
    FILE *f,        // file to read from, must already be open
    int dtype,      // CHOLMOD_DOUBLE or CHOLMOD_SINGLE
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_read_sparse2 (FILE *, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_triplet: read a triplet matrix from a file (double only)
//------------------------------------------------------------------------------

cholmod_triplet *cholmod_read_triplet   // return triplet matrix (double)
(
    // input:
    FILE *f,        // file to read from, must already be open
    cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_read_triplet (FILE *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_triplet: read a triplet matrix from a file (float or double)
//------------------------------------------------------------------------------

cholmod_triplet *cholmod_read_triplet2  // return triplet matrix (double/single)
(
    // input:
    FILE *f,        // file to read from, must already be open
    int dtype,      // CHOLMOD_DOUBLE or CHOLMOD_SINGLE
    cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_read_triplet2 (FILE *, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_dense: read a dense matrix from a file (double only)
//------------------------------------------------------------------------------

cholmod_dense *cholmod_read_dense   // return dense matrix (double)
(
    // input:
    FILE *f,        // file to read from, must already be open
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_read_dense (FILE *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_dense2: read a dense matrix from a file (float or double)
//------------------------------------------------------------------------------

cholmod_dense *cholmod_read_dense2  // return dense matrix (double/single)
(
    // input:
    FILE *f,        // file to read from, must already be open
    int dtype,      // CHOLMOD_DOUBLE or CHOLMOD_SINGLE
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_read_dense2 (FILE *, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_matrix: read a sparse or dense matrix from a file (double only)
//------------------------------------------------------------------------------

void *cholmod_read_matrix   // return sparse/triplet/double matrix (double)
(
    // input:
    FILE *f,        // file to read from, must already be open
    int prefer,     // If 0, a sparse matrix is always return as a
                    // cholmod_triplet form.  It can have any stype
                    // (symmetric-lower, unsymmetric, or symmetric-upper).
                    // If 1, a sparse matrix is returned as an unsymmetric
                    // cholmod_sparse form (A->stype == 0), with both upper and
                    // lower triangular parts present.  This is what the MATLAB
                    // mread mexFunction does, since MATLAB does not have an
                    // stype.
                    // If 2, a sparse matrix is returned with an stype of 0 or
                    // 1 (unsymmetric, or symmetric with upper part stored).
                    // This argument has no effect for dense matrices.
    // output:
    int *mtype,     // CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE
    cholmod_common *Common
) ;
void *cholmod_l_read_matrix (FILE *, int, int *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_read_matrix2: read a sparse or dense matrix (float or double)
//------------------------------------------------------------------------------

void *cholmod_read_matrix2  // sparse/triplet/double matrix (double/single)
(
    // input:
    FILE *f,        // file to read from, must already be open
    int prefer,     // see cholmod_read_matrix
    int dtype,      // CHOLMOD_DOUBLE or CHOLMOD_SINGLE
    // output:
    int *mtype,     // CHOLMOD_TRIPLET, CHOLMOD_SPARSE or CHOLMOD_DENSE
    cholmod_common *Common
) ;
void *cholmod_l_read_matrix2 (FILE *, int, int, int *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_write_sparse: write a sparse matrix to a file
//------------------------------------------------------------------------------

// return values of cholmod_symmetry and cholmod_write:
#define CHOLMOD_MM_RECTANGULAR       1
#define CHOLMOD_MM_UNSYMMETRIC       2
#define CHOLMOD_MM_SYMMETRIC         3
#define CHOLMOD_MM_HERMITIAN         4
#define CHOLMOD_MM_SKEW_SYMMETRIC    5
#define CHOLMOD_MM_SYMMETRIC_POSDIAG 6
#define CHOLMOD_MM_HERMITIAN_POSDIAG 7

int cholmod_write_sparse    // see above, or -1 on error
(
    // input:
    FILE *f,                // file to write to, must already be open
    cholmod_sparse *A,      // matrix to print
    cholmod_sparse *Z,      // optional matrix with pattern of explicit zeros
    const char *comments,   // optional filename of comments to include
    cholmod_common *Common
) ;
int cholmod_l_write_sparse (FILE *, cholmod_sparse *, cholmod_sparse *,
    const char *c, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_write_dense: write a dense matrix to a file
//------------------------------------------------------------------------------

int cholmod_write_dense     // CHOLMOD_MM_UNSYMMETRIC or _RECTANGULAR, or
(                           // -1 on error
    // input:
    FILE *f,                // file to write to, must already be open
    cholmod_dense *X,       // matrix to print
    const char *comments,   // optional filename of comments to include
    cholmod_common *Common
) ;
int cholmod_l_write_dense (FILE *, cholmod_dense *, const char *,
    cholmod_common *) ;

#endif

//==============================================================================
// CHOLMOD:Cholesky Module
//==============================================================================

#ifndef NCHOLESKY

// Sparse Cholesky routines: analysis, factorization, and solve.
//
// The primary routines are all that a user requires to order, analyze, and
// factorize a sparse symmetric positive definite matrix A (or A*A'), and
// to solve Ax=b (or A*A'x=b).  The primary routines rely on the secondary
// routines, the CHOLMOD Utility module, and the AMD and COLAMD packages.  They
// make optional use of the CHOLMOD Supernodal and Partition modules, the
// METIS package, and the CCOLAMD package.
//
// Primary routines:
// -----------------
//
// cholmod_analyze              order and analyze (simplicial or supernodal)
// cholmod_factorize            simplicial or supernodal Cholesky factorization
// cholmod_solve                solve a linear system (simplicial or supernodal)
// cholmod_solve2               like cholmod_solve, but reuse workspace
// cholmod_spsolve              solve a linear system (sparse x and b)
//
// Secondary routines:
// ------------------
//
// cholmod_analyze_p            analyze, with user-provided permutation or f set
// cholmod_factorize_p          factorize, with user-provided permutation or f
// cholmod_analyze_ordering     analyze a fill-reducing ordering
// cholmod_etree                find the elimination tree
// cholmod_rowcolcounts         compute the row/column counts of L
// cholmod_amd                  order using AMD
// cholmod_colamd               order using COLAMD
// cholmod_rowfac               incremental simplicial factorization
// cholmod_rowfac_mask          rowfac, specific to LPDASA
// cholmod_rowfac_mask2         rowfac, specific to LPDASA
// cholmod_row_subtree          find the nonzero pattern of a row of L
// cholmod_resymbol             recompute the symbolic pattern of L
// cholmod_resymbol_noperm      recompute the symbolic pattern of L, no L->Perm
// cholmod_postorder            postorder a tree
//
// Requires the Utility module, and two packages: AMD and COLAMD.
// Optionally uses the Supernodal and Partition modules.
// Required by the Partition module.

//------------------------------------------------------------------------------
// cholmod_analyze:  order and analyze (simplicial or supernodal)
//------------------------------------------------------------------------------

// Orders and analyzes A, AA', PAP', or PAA'P' and returns a symbolic factor
// that can later be passed to cholmod_factorize.

cholmod_factor *cholmod_analyze     // returns symbolic factor L
(
    // input:
    cholmod_sparse *A,      // matrix to order and analyze
    cholmod_common *Common
) ;
cholmod_factor *cholmod_l_analyze (cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_analyze_p:  analyze, with user-provided permutation or f set
//------------------------------------------------------------------------------

// Orders and analyzes A, AA', PAP', PAA'P', FF', or PFF'P and returns a
// symbolic factor that can later be passed to cholmod_factorize, where
// F = A(:,fset) if fset is not NULL and A->stype is zero.
// UserPerm is tried if non-NULL.

cholmod_factor *cholmod_analyze_p   // returns symbolic factor L
(
    // input:
    cholmod_sparse *A,  // matrix to order and analyze
    int32_t *UserPerm,  // user-provided permutation, size A->nrow
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    cholmod_common *Common
) ;
cholmod_factor *cholmod_l_analyze_p (cholmod_sparse *, int64_t *, int64_t *,
    size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_analyze_p2:  analyze for sparse Cholesky or sparse QR
//------------------------------------------------------------------------------

// This is normally not need by the user application.

cholmod_factor *cholmod_analyze_p2
(
    // input:
    int for_whom,       // FOR_SPQR     (0): for SPQR but not GPU-accelerated
                        // FOR_CHOLESKY (1): for Cholesky (GPU or not)
                        // FOR_SPQRGPU  (2): for SPQR with GPU acceleration
    cholmod_sparse *A,  // matrix to order and analyze
    int32_t *UserPerm,  // user-provided permutation, size A->nrow
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    cholmod_common *Common
) ;
cholmod_factor *cholmod_l_analyze_p2 (int, cholmod_sparse *, int64_t *,
    int64_t *, size_t, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_factorize:  simplicial or supernodal Cholesky factorization
//------------------------------------------------------------------------------

// Factorizes PAP' (or PAA'P' if A->stype is 0), using a factor obtained
// from cholmod_analyze.  The analysis can be re-used simply by calling this
// routine a second time with another matrix.  A must have the same nonzero
// pattern as that passed to cholmod_analyze.

int cholmod_factorize       // simplicial or superodal Cholesky factorization
(
    // input:
    cholmod_sparse *A,  // matrix to factorize
    // input/output:
    cholmod_factor *L,  // resulting factorization
    cholmod_common *Common
) ;
int cholmod_l_factorize (cholmod_sparse *, cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_factorize_p:  factorize, with user-provided permutation or fset
//------------------------------------------------------------------------------

// Same as cholmod_factorize, but with more options.

int cholmod_factorize_p
(
    // input:
    cholmod_sparse *A,  // matrix to factorize
    double beta [2],    // factorize beta*I+A or beta*I+A'*A
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    // input/output:
    cholmod_factor *L,  // resulting factorization
    cholmod_common *Common
) ;
int cholmod_l_factorize_p (cholmod_sparse *, double [2], int64_t *, size_t,
    cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_solve:  solve a linear system (simplicial or supernodal)
//------------------------------------------------------------------------------

// Solves one of many linear systems with a dense right-hand-side, using the
// factorization from cholmod_factorize (or as modified by any other CHOLMOD
// routine).  D is identity for LL' factorizations.

#define CHOLMOD_A    0  /* solve Ax=b    */
#define CHOLMOD_LDLt 1  /* solve LDL'x=b */
#define CHOLMOD_LD   2  /* solve LDx=b   */
#define CHOLMOD_DLt  3  /* solve DL'x=b  */
#define CHOLMOD_L    4  /* solve Lx=b    */
#define CHOLMOD_Lt   5  /* solve L'x=b   */
#define CHOLMOD_D    6  /* solve Dx=b    */
#define CHOLMOD_P    7  /* permute x=Px  */
#define CHOLMOD_Pt   8  /* permute x=P'x */

cholmod_dense *cholmod_solve    // returns the solution X
(
    // input:
    int sys,            // system to solve
    cholmod_factor *L,  // factorization to use
    cholmod_dense *B,   // right-hand-side
    cholmod_common *Common
) ;
cholmod_dense *cholmod_l_solve (int, cholmod_factor *, cholmod_dense *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_solve2:  like cholmod_solve, but with reusable workspace
//------------------------------------------------------------------------------

int cholmod_solve2     // returns TRUE on success, FALSE on failure
(
    // input:
    int sys,                        // system to solve
    cholmod_factor *L,              // factorization to use
    cholmod_dense *B,               // right-hand-side
    cholmod_sparse *Bset,
    // output:
    cholmod_dense **X_Handle,       // solution, allocated if need be
    cholmod_sparse **Xset_Handle,
    // workspace:
    cholmod_dense **Y_Handle,       // workspace, or NULL
    cholmod_dense **E_Handle,       // workspace, or NULL
    cholmod_common *Common
) ;
int cholmod_l_solve2 (int, cholmod_factor *, cholmod_dense *, cholmod_sparse *,
    cholmod_dense **, cholmod_sparse **, cholmod_dense **, cholmod_dense **,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_spsolve:  solve a linear system with a sparse right-hand-side
//------------------------------------------------------------------------------

cholmod_sparse *cholmod_spsolve             // returns the sparse solution X
(
    // input:
    int sys,            // system to solve
    cholmod_factor *L,  // factorization to use
    cholmod_sparse *B,  // right-hand-side
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_spsolve (int, cholmod_factor *, cholmod_sparse *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_etree: find the elimination tree of A or A'*A
//------------------------------------------------------------------------------

int cholmod_etree
(
    // input:
    cholmod_sparse *A,
    // output:
    int32_t *Parent,      // size ncol.  Parent [j] = p if p is the parent of j
    cholmod_common *Common
) ;
int cholmod_l_etree (cholmod_sparse *, int64_t *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowcolcounts: compute the row/column counts of L
//------------------------------------------------------------------------------

int cholmod_rowcolcounts
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int32_t *Parent,    // size nrow.  Parent [i] = p if p is the parent of i
    int32_t *Post,      // size nrow.  Post [k] = i if i is the kth node in
                        // the postordered etree.
    // output:
    int32_t *RowCount,  // size nrow. RowCount [i] = # entries in the ith
                        // row of L, including the diagonal.
    int32_t *ColCount,  // size nrow. ColCount [i] = # entries in the ith
                        // column of L, including the diagonal.
    int32_t *First,     // size nrow.  First [i] = k is the least
                        // postordering of any descendant of i.
    int32_t *Level,     // size nrow.  Level [i] is the length of the path
                        // from i to the root, with Level [root] = 0.
    cholmod_common *Common
) ;
int cholmod_l_rowcolcounts (cholmod_sparse *, int64_t *, size_t, int64_t *,
    int64_t *, int64_t *, int64_t *, int64_t *, int64_t *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_analyze_ordering:  analyze a fill-reducing ordering
//------------------------------------------------------------------------------

int cholmod_analyze_ordering
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    int ordering,       // ordering method used
    int32_t *Perm,      // size n, fill-reducing permutation to analyze
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    // output:
    int32_t *Parent,    // size n, elimination tree
    int32_t *Post,      // size n, postordering of elimination tree
    int32_t *ColCount,  // size n, nnz in each column of L
    // workspace:
    int32_t *First,     // size n workspace for cholmod_postorder
    int32_t *Level,     // size n workspace for cholmod_postorder
    cholmod_common *Common
) ;
int cholmod_l_analyze_ordering (cholmod_sparse *, int, int64_t *, int64_t *,
    size_t, int64_t *, int64_t *, int64_t *, int64_t *, int64_t *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_amd:  order using AMD
//------------------------------------------------------------------------------

// Finds a permutation P to reduce fill-in in the factorization of P*A*P'
// or P*A*A'P'

int cholmod_amd
(
    // input:
    cholmod_sparse *A,  // matrix to order
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    // output:
    int32_t *Perm,      // size A->nrow, output permutation
    cholmod_common *Common
) ;
int cholmod_l_amd (cholmod_sparse *, int64_t *, size_t, int64_t *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_colamd:  order using COLAMD
//------------------------------------------------------------------------------

// Finds a permutation P to reduce fill-in in the factorization of P*A*A'*P'.
// Orders F*F' where F = A (:,fset) if fset is not NULL

int cholmod_colamd
(
    // input:
    cholmod_sparse *A,  // matrix to order
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int postorder,      // if TRUE, follow with a coletree postorder
    // output:
    int32_t *Perm,      // size A->nrow, output permutation
    cholmod_common *Common
) ;
int cholmod_l_colamd (cholmod_sparse *, int64_t *, size_t, int, int64_t *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowfac:  incremental simplicial factorization
//------------------------------------------------------------------------------

// Partial or complete simplicial factorization.  Rows and columns kstart:kend-1
// of L and D must be initially equal to rows/columns kstart:kend-1 of the
// identity matrix.   Row k can only be factorized if all descendants of node
// k in the elimination tree have been factorized.

int cholmod_rowfac 
(
    // input:
    cholmod_sparse *A,  // matrix to factorize
    cholmod_sparse *F,  // used for A*A' case only. F=A' or A(:,f)'
    double beta [2],    // factorize beta*I+A or beta*I+AA'
    size_t kstart,      // first row to factorize
    size_t kend,        // last row to factorize is kend-1
    // input/output:
    cholmod_factor *L,
    cholmod_common *Common
) ;
int cholmod_l_rowfac (cholmod_sparse *, cholmod_sparse *, double [2], size_t,
    size_t, cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowfac_mask:  incremental simplicial factorization
//------------------------------------------------------------------------------

// cholmod_rowfac_mask and cholmod_rowfac_mask2 are version of cholmod_rowfac
// that are specific to LPDASA.  It is unlikely to be needed by any other
// application, and is not documented in the CHOLMOD User Guide.

int cholmod_rowfac_mask
(
    // input:
    cholmod_sparse *A,  // matrix to factorize
    cholmod_sparse *F,  // used for A*A' case only. F=A' or A(:,f)'
    double beta [2],    // factorize beta*I+A or beta*I+AA'
    size_t kstart,      // first row to factorize
    size_t kend,        // last row to factorize is kend-1
    int32_t *mask,      // size A->nrow. if mask[i] >= 0 row i is set to zero
    int32_t *RLinkUp,   // size A->nrow. link list of rows to compute
    // input/output:
    cholmod_factor *L,
    cholmod_common *Common
) ;
int cholmod_l_rowfac_mask (cholmod_sparse *, cholmod_sparse *, double [2],
    size_t, size_t, int64_t *, int64_t *, cholmod_factor *, cholmod_common *) ;

int cholmod_rowfac_mask2
(
    // input:
    cholmod_sparse *A,  // matrix to factorize
    cholmod_sparse *F,  // used for A*A' case only. F=A' or A(:,f)'
    double beta [2],    // factorize beta*I+A or beta*I+AA'
    size_t kstart,      // first row to factorize
    size_t kend,        // last row to factorize is kend-1
    int32_t *mask,      // size A->nrow. if mask[i] >= maskmark row i is set
                        // to zero
    int32_t maskmark,   // for mask [i] test
    int32_t *RLinkUp,   // size A->nrow. link list of rows to compute
    // input/output:
    cholmod_factor *L,
    cholmod_common *Common
) ;
int cholmod_l_rowfac_mask2 (cholmod_sparse *, cholmod_sparse *, double [2],
    size_t, size_t, int64_t *, int64_t, int64_t *, cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_row_subtree:  find the nonzero pattern of a row of L
//------------------------------------------------------------------------------

// Find the nonzero pattern of x for the system Lx=b where L = (0:k-1,0:k-1)
// and b = kth column of A or A*A' (rows 0 to k-1 only)

int cholmod_row_subtree
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    cholmod_sparse *F,  // used for A*A' case only. F=A' or A(:,f)'
    size_t krow,        // row k of L
    int32_t *Parent,    // elimination tree
    // output:
    cholmod_sparse *R,  // pattern of L(k,:), 1-by-n with R->nzmax >= n
    cholmod_common *Common
) ;
int cholmod_l_row_subtree (cholmod_sparse *, cholmod_sparse *, size_t,
    int64_t *, cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_lsolve_pattern: find the nonzero pattern of y=L\b
//------------------------------------------------------------------------------

int cholmod_lsolve_pattern
(
    // input:
    cholmod_sparse *B,  // sparse right-hand-side (a single sparse column)
    cholmod_factor *L,  // the factor L from which parent(i) is derived
    // output:
    cholmod_sparse *Yset,   // pattern of Y=L\B, n-by-1 with Y->nzmax >= n
    cholmod_common *Common
) ;
int cholmod_l_lsolve_pattern (cholmod_sparse *, cholmod_factor *,
    cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_row_lsubtree:  find the nonzero pattern of a row of L
//------------------------------------------------------------------------------

// Identical to cholmod_row_subtree, except that it finds the elimination tree
// from L itself.

int cholmod_row_lsubtree
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    int32_t *Fi,        // nonzero pattern of kth row of A', not required
                        // for the symmetric case.  Need not be sorted.
    size_t fnz,         // size of Fi
    size_t krow,        // row k of L
    cholmod_factor *L,  // the factor L from which parent(i) is derived
    // output:
    cholmod_sparse *R,  // pattern of L(k,:), n-by-1 with R->nzmax >= n
    cholmod_common *Common
) ;
int cholmod_l_row_lsubtree (cholmod_sparse *, int64_t *, size_t, size_t,
    cholmod_factor *, cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_resymbol:  recompute the symbolic pattern of L
//------------------------------------------------------------------------------

// Remove entries from L that are not in the factorization of P*A*P', P*A*A'*P',
// or P*F*F'*P' (depending on A->stype and whether fset is NULL or not).
//
// cholmod_resymbol is the same as cholmod_resymbol_noperm, except that it
// first permutes A according to L->Perm.  A can be upper/lower/unsymmetric,
// in contrast to cholmod_resymbol_noperm (which can be lower or unsym).

int cholmod_resymbol    // recompute symbolic pattern of L
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    int *fset,          // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int pack,           // if TRUE, pack the columns of L
    // input/output:
    cholmod_factor *L,  // factorization, entries pruned on output
    cholmod_common *Common
) ;
int cholmod_l_resymbol (cholmod_sparse *, int64_t *, size_t, int,
    cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_resymbol_noperm:  recompute the symbolic pattern of L, no L->Perm
//------------------------------------------------------------------------------

// Remove entries from L that are not in the factorization of A, A*A',
// or F*F' (depending on A->stype and whether fset is NULL or not).

int cholmod_resymbol_noperm
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int pack,           // if TRUE, pack the columns of L
    // input/output:
    cholmod_factor *L,  // factorization, entries pruned on output
    cholmod_common *Common
) ;
int cholmod_l_resymbol_noperm (cholmod_sparse *, int64_t *, size_t, int,
    cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rcond:  compute rough estimate of reciprocal of condition number
//------------------------------------------------------------------------------

double cholmod_rcond        // return rcond estimate
(
    // input:
    cholmod_factor *L,      // factorization to query; not modified
    cholmod_common *Common
) ;
double cholmod_l_rcond (cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_postorder: Compute the postorder of a tree
//------------------------------------------------------------------------------

int32_t cholmod_postorder   // return # of nodes postordered
(
    // input:
    int32_t *Parent,    // size n. Parent [j] = p if p is the parent of j
    size_t n,
    int32_t *Weight,    // size n, optional. Weight [j] is weight of node j
    // output:
    int32_t *Post,      // size n. Post [k] = j is kth in postordered tree
    cholmod_common *Common
) ;
int64_t cholmod_l_postorder (int64_t *, size_t, int64_t *, int64_t *,
    cholmod_common *) ;

#endif

//==============================================================================
// CHOLMOD:MatrixOps Module
//==============================================================================

#ifndef NMATRIXOPS

// Basic operations on sparse and dense matrices.
//
// cholmod_drop             A = entries in A with abs. value >= tol
// cholmod_norm_dense       s = norm (X), 1-norm, inf-norm, or 2-norm
// cholmod_norm_sparse      s = norm (A), 1-norm or inf-norm
// cholmod_horzcat          C = [A,B]
// cholmod_scale            A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s)
// cholmod_sdmult           Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y
// cholmod_ssmult           C = A*B
// cholmod_submatrix        C = A (i,j), where i and j are arbitrary vectors
// cholmod_vertcat          C = [A ; B]
//
// A, B, C: sparse matrices (cholmod_sparse)
// X, Y: dense matrices (cholmod_dense)
// s: scalar or vector
//
// Requires the Utility module.  Not required by any other CHOLMOD module.

//------------------------------------------------------------------------------
// cholmod_drop:  drop entries with small absolute value
//------------------------------------------------------------------------------

int cholmod_drop
(
    // input:
    double tol,         // keep entries with absolute value > tol
    // input/output:
    cholmod_sparse *A,  // matrix to drop entries from
    cholmod_common *Common
) ;
int cholmod_l_drop (double, cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_norm_dense:  s = norm (X), 1-norm, inf-norm, or 2-norm
//------------------------------------------------------------------------------

double cholmod_norm_dense       // returns norm (X)
(
    // input:
    cholmod_dense *X,   // matrix to compute the norm of
    int norm,           // type of norm: 0: inf. norm, 1: 1-norm, 2: 2-norm
    cholmod_common *Common
) ;
double cholmod_l_norm_dense (cholmod_dense *, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_norm_sparse:  s = norm (A), 1-norm or inf-norm
//------------------------------------------------------------------------------

double cholmod_norm_sparse          // returns norm (A)
(
    // input:
    cholmod_sparse *A,  // matrix to compute the norm of
    int norm,           // type of norm: 0: inf. norm, 1: 1-norm
    cholmod_common *Common
) ;
double cholmod_l_norm_sparse (cholmod_sparse *, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_horzcat:  C = [A,B]
//------------------------------------------------------------------------------

// C is returned as an unsymmetric matrix with C->stype of zero.  If A and/or
// B are symmetric, they are converted first to unsymmetric, and the conversion
// is governed by the mode input parameter.

cholmod_sparse *cholmod_horzcat     // returns C = [A B]
(
    // input:
    cholmod_sparse *A,  // left matrix to concatenate
    cholmod_sparse *B,  // right matrix to concatenate
    int mode,           // 2: numerical (conj) if A and/or B are symmetric,
                        // 1: numerical (non-conj.) if A and/or B are symmetric.
                        // 0: pattern
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_horzcat (cholmod_sparse *, cholmod_sparse *, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_scale:  A = diag(s)*A, A*diag(s), s*A or diag(s)*A*diag(s)
//------------------------------------------------------------------------------

// scaling modes, selected by the scale input parameter:
#define CHOLMOD_SCALAR 0    /* A = s*A               */
#define CHOLMOD_ROW    1    /* A = diag(s)*A         */
#define CHOLMOD_COL    2    /* A = A*diag(s)         */
#define CHOLMOD_SYM    3    /* A = diag(s)*A*diag(s) */

int cholmod_scale
(
    // input:
    cholmod_dense *S,   // scale factors (scalar or vector)
    int scale,          // type of scaling to compute
    // input/output:
    cholmod_sparse *A,  // matrix to scale
    cholmod_common *Common
) ;
int cholmod_l_scale (cholmod_dense *, int, cholmod_sparse *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_sdmult:  Y = alpha*(A*X) + beta*Y or alpha*(A'*X) + beta*Y
//------------------------------------------------------------------------------

// Sparse matrix times dense matrix

int cholmod_sdmult
(
    // input:
    cholmod_sparse *A,  // sparse matrix to multiply
    int transpose,      // use A if 0, otherwise use A'
    double alpha [2],   // scale factor for A
    double beta [2],    // scale factor for Y
    cholmod_dense *X,   // dense matrix to multiply
    // input/output:
    cholmod_dense *Y,   // resulting dense matrix
    cholmod_common *Common
) ;
int cholmod_l_sdmult (cholmod_sparse *, int, double [2], double [2],
    cholmod_dense *, cholmod_dense *Y, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_ssmult:  C = A*B
//------------------------------------------------------------------------------

// Sparse matrix times sparse matrix.

// If A and/or B are symmetric, they are converted first to unsymmetric, and
// the conversion is governed by the mode input parameter.

cholmod_sparse *cholmod_ssmult      // return C=A*B
(
    // input:
    cholmod_sparse *A,  // left matrix to multiply
    cholmod_sparse *B,  // right matrix to multiply
    int stype,          // requested stype of C
    int mode,           // 2: numerical (conj) if A and/or B are symmetric,
                        // 1: numerical (non-conj.) if A and/or B are symmetric.
                        // 0: pattern
    int sorted,         // if TRUE then return C with sorted columns
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_ssmult (cholmod_sparse *, cholmod_sparse *, int, int,
    int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_submatrix:  C = A (r,c), where i and j are arbitrary vectors
//------------------------------------------------------------------------------

// rsize < 0 denotes ":" in MATLAB notation, or more precisely 0:(A->nrow)-1.
// In this case, r can be NULL.  An rsize of zero, or r = NULL and rsize >= 0,
// denotes "[ ]" in MATLAB notation (the empty set).
// Similar rules hold for csize.

// C is returned as an unsymmetric matrix with C->stype of zero.  If A and/or
// B are symmetric, they are converted first to unsymmetric, and the conversion
// is governed by the mode input parameter.

cholmod_sparse *cholmod_submatrix   // return C = A (rset,cset)
(
    // input:
    cholmod_sparse *A,  // matrix to subreference
    int32_t *rset,      // set of row indices, duplicates OK
    int64_t rsize,      // size of rset, or -1 for ":"
    int32_t *cset,      // set of column indices, duplicates OK
    int64_t csize,      // size of cset, or -1 for ":"
    int mode,           // 2: numerical (conj) if A and/or B are symmetric,
                        // 1: numerical (non-conj.) if A and/or B are symmetric.
                        // 0: pattern
    int sorted,         // if TRUE then return C with sorted columns
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_submatrix (cholmod_sparse *, int64_t *,
    int64_t, int64_t *, int64_t, int, int, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_vertcat:  C = [A ; B]
//------------------------------------------------------------------------------

// C is returned as an unsymmetric matrix with C->stype of zero.  If A and/or
// B are symmetric, they are converted first to unsymmetric, and the conversion
// is governed by the mode input parameter.

cholmod_sparse *cholmod_vertcat     // returns C = [A ; B]
(
    // input:
    cholmod_sparse *A,  // top matrix to concatenate
    cholmod_sparse *B,  // bottom matrix to concatenate
    int mode,           // 2: numerical (conj) if A and/or B are symmetric,
                        // 1: numerical (non-conj.) if A and/or B are symmetric
                        // 0: pattern
    cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_vertcat (cholmod_sparse *, cholmod_sparse *, int,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_symmetry: determine if a sparse matrix is symmetric
//------------------------------------------------------------------------------

// return values of cholmod_symmetry and cholmod_write:
// #define CHOLMOD_MM_RECTANGULAR       1
// #define CHOLMOD_MM_UNSYMMETRIC       2
// #define CHOLMOD_MM_SYMMETRIC         3
// #define CHOLMOD_MM_HERMITIAN         4
// #define CHOLMOD_MM_SKEW_SYMMETRIC    5
// #define CHOLMOD_MM_SYMMETRIC_POSDIAG 6
// #define CHOLMOD_MM_HERMITIAN_POSDIAG 7

int cholmod_symmetry            // returns the matrix symmetry (see above)
(
    // input:
    cholmod_sparse *A,
    int option,                 // option 0, 1, or 2
    // output:
    int32_t *xmatched,          // # of matched numerical entries
    int32_t *pmatched,          // # of matched entries in pattern
    int32_t *nzoffdiag,         // # of off diagonal entries
    int32_t *nzdiag,            // # of diagonal entries
    cholmod_common *Common
) ;
int cholmod_l_symmetry (cholmod_sparse *, int, int64_t *, int64_t *, int64_t *,
    int64_t *, cholmod_common *) ;

#endif

//==============================================================================
// CHOLMOD:Modify Module
//==============================================================================

#ifndef NMODIFY

//------------------------------------------------------------------------------
// CHOLMOD:Modify Module. Copyright (C) 2005-2023, Timothy A. Davis and William
// W. Hager.  http://www.suitesparse.com
//------------------------------------------------------------------------------

// Sparse Cholesky modification routines: update / downdate / rowadd / rowdel.
// Can also modify a corresponding solution to Lx=b when L is modified.  This
// module is most useful when applied on a Cholesky factorization computed by
// the Cholesky module, but it does not actually require the Cholesky module.
// The Utility module can create an identity Cholesky factorization (LDL' where
// L=D=I) that can then by modified by these routines.
//
// Primary routines:
// -----------------
//
// cholmod_updown           multiple rank update/downdate
// cholmod_rowadd           add a row to an LDL' factorization
// cholmod_rowdel           delete a row from an LDL' factorization
//
// Secondary routines:
// -------------------
//
// cholmod_updown_solve     update/downdate, and modify solution to Lx=b
// cholmod_updown_mark      update/downdate, and modify solution to partial Lx=b
// cholmod_updown_mask      update/downdate for LPDASA
// cholmod_updown_mask2     update/downdate for LPDASA
// cholmod_rowadd_solve     add a row, and update solution to Lx=b
// cholmod_rowadd_mark      add a row, and update solution to partial Lx=b
// cholmod_rowdel_solve     delete a row, and downdate Lx=b
// cholmod_rowdel_mark      delete a row, and downdate solution to partial Lx=b
//
// Requires the Utility module.  Not required by any other CHOLMOD module.

//------------------------------------------------------------------------------
// cholmod_updown:  multiple rank update/downdate
//------------------------------------------------------------------------------

// Compute the new LDL' factorization of LDL'+CC' (an update) or LDL'-CC'
// (a downdate).  The factor object L need not be an LDL' factorization; it
// is converted to one if it isn't.

int cholmod_updown          // update/downdate
(
    // input:
    int update,         // TRUE for update, FALSE for downdate
    cholmod_sparse *C,  // the incoming sparse update
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_common *Common
) ;
int cholmod_l_updown (int, cholmod_sparse *, cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_updown_solve:  update/downdate, and modify solution to Lx=b
//------------------------------------------------------------------------------

// Does the same as cholmod_updown, except that it also updates/downdates the
// solution to Lx=b+DeltaB.  x and b must be n-by-1 dense matrices.  b is not
// need as input to this routine, but a sparse change to b is (DeltaB).  Only
// entries in DeltaB corresponding to columns modified in L are accessed; the
// rest must be zero.

int cholmod_updown_solve
(
    // input:
    int update,         // TRUE for update, FALSE for downdate
    cholmod_sparse *C,  // the incoming sparse update
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_updown_solve (int, cholmod_sparse *, cholmod_factor *,
    cholmod_dense *, cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_updown_mark:  update/downdate, and modify solution to partial Lx=b
//------------------------------------------------------------------------------

// Does the same as cholmod_updown_solve, except only part of L is used in
// the update/downdate of the solution to Lx=b.  This routine is an "expert"
// routine.  It is meant for use in LPDASA only.  See cholmod_updown.c for
// a description of colmark.

int cholmod_updown_mark
(
    // input:
    int update,         // TRUE for update, FALSE for downdate
    cholmod_sparse *C,  // the incoming sparse update
    int32_t *colmark,   // array of size n.  See cholmod_updown.c for details
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_updown_mark (int, cholmod_sparse *, int64_t *, cholmod_factor *,
    cholmod_dense *, cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_updown_mask:  update/downdate, for LPDASA
//------------------------------------------------------------------------------

// Does the same as cholmod_updown_mark, except has an additional "mask"
// argument.  This routine is an "expert" routine.  It is meant for use in
// LPDASA only.  See cholmod_updown.c for a description of mask.

int cholmod_updown_mask
(
    // input:
    int update,         // TRUE for update, FALSE for downdate
    cholmod_sparse *C,  // the incoming sparse update
    int32_t *colmark,   // array of size n.  See cholmod_updown.c for details
    int32_t *mask,      // size n
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_updown_mask (int, cholmod_sparse *, int64_t *, int64_t *,
    cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;

int cholmod_updown_mask2
(
    // input:
    int update,         // TRUE for update, FALSE for downdate
    cholmod_sparse *C,  // the incoming sparse update
    int32_t *colmark,   // array of size n.  See cholmod_updown.c for details
    int32_t *mask,      // size n
    int32_t maskmark,
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_updown_mask2 (int, cholmod_sparse *, int64_t *, int64_t *,
    int64_t, cholmod_factor *, cholmod_dense *, cholmod_dense *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowadd:  add a row to an LDL' factorization (a rank-2 update)
//------------------------------------------------------------------------------

// cholmod_rowadd adds a row to the LDL' factorization.  It computes the kth
// row and kth column of L, and then updates the submatrix L (k+1:n,k+1:n)
// accordingly.  The kth row and column of L must originally be equal to the
// kth row and column of the identity matrix.  The kth row/column of L is
// computed as the factorization of the kth row/column of the matrix to
// factorize, which is provided as a single n-by-1 sparse matrix R.

int cholmod_rowadd      // add a row to an LDL' factorization
(
    // input:
    size_t k,           // row/column index to add
    cholmod_sparse *R,  // row/column of matrix to factorize (n-by-1)
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_common *Common
) ;
int cholmod_l_rowadd (size_t, cholmod_sparse *, cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowadd_solve:  add a row, and update solution to Lx=b
//------------------------------------------------------------------------------

// Does the same as cholmod_rowadd, and also updates the solution to Lx=b
// See cholmod_updown for a description of how Lx=b is updated.  There is on
// additional parameter:  bk specifies the new kth entry of b.

int cholmod_rowadd_solve
(
    // input:
    size_t k,           // row/column index to add
    cholmod_sparse *R,  // row/column of matrix to factorize (n-by-1)
    double bk [2],      // kth entry of the right-hand-side b
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_rowadd_solve (size_t, cholmod_sparse *, double [2],
    cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowadd_mark:  add a row, and update solution to partial Lx=b
//------------------------------------------------------------------------------

// Does the same as cholmod_rowadd_solve, except only part of L is used in
// the update/downdate of the solution to Lx=b.  This routine is an "expert"
// routine.  It is meant for use in LPDASA only.

int cholmod_rowadd_mark
(
    // input:
    size_t k,           // row/column index to add
    cholmod_sparse *R,  // row/column of matrix to factorize (n-by-1)
    double bk [2],      // kth entry of the right hand side, b
    int32_t *colmark,   // int32_t array of size 1.  See cholmod_updown.c
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_rowadd_mark (size_t, cholmod_sparse *, double [2], int64_t *,
    cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowdel:  delete a row from an LDL' factorization (a rank-2 update)
//------------------------------------------------------------------------------

// Sets the kth row and column of L to be the kth row and column of the identity
// matrix, and updates L(k+1:n,k+1:n) accordingly.   To reduce the running time,
// the caller can optionally provide the nonzero pattern (or an upper bound) of
// kth row of L, as the sparse n-by-1 vector R.  Provide R as NULL if you want
// CHOLMOD to determine this itself, which is easier for the caller, but takes
// a little more time.

int cholmod_rowdel      // delete a rw from an LDL' factorization
(
    // input:
    size_t k,           // row/column index to delete
    cholmod_sparse *R,  // NULL, or the nonzero pattern of kth row of L
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_common *Common
) ;
int cholmod_l_rowdel (size_t, cholmod_sparse *, cholmod_factor *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowdel_solve:  delete a row, and downdate Lx=b
//------------------------------------------------------------------------------

// Does the same as cholmod_rowdel, but also downdates the solution to Lx=b.
// When row/column k of A is "deleted" from the system A*y=b, this can induce
// a change to x, in addition to changes arising when L and b are modified.
// If this is the case, the kth entry of y is required as input (yk).

int cholmod_rowdel_solve
(
    // input:
    size_t k,           // row/column index to delete
    cholmod_sparse *R,  // NULL, or the nonzero pattern of kth row of L
    double yk [2],      // kth entry in the solution to A*y=b
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_rowdel_solve (size_t, cholmod_sparse *, double [2],
    cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_rowdel_mark:  delete a row, and downdate solution to partial Lx=b
//------------------------------------------------------------------------------

// Does the same as cholmod_rowdel_solve, except only part of L is used in
// the update/downdate of the solution to Lx=b.  This routine is an "expert"
// routine.  It is meant for use in LPDASA only.

int cholmod_rowdel_mark
(
    // input:
    size_t k,           // row/column index to delete
    cholmod_sparse *R,  // NULL, or the nonzero pattern of kth row of L
    double yk [2],      // kth entry in the solution to A*y=b
    int32_t *colmark,   // int32_t array of size 1.  See cholmod_updown.c
    // input/output:
    cholmod_factor *L,  // factor to modify
    cholmod_dense *X,   // solution to Lx=b (size n-by-1)
    cholmod_dense *DeltaB,  // change in b, zero on output
    cholmod_common *Common
) ;
int cholmod_l_rowdel_mark (size_t, cholmod_sparse *, double [2], int64_t *,
    cholmod_factor *, cholmod_dense *, cholmod_dense *, cholmod_common *) ;

#endif

//==============================================================================
// CHOLMOD:Partition Module (CAMD, CCOLAMD, and CSYMAMD)
//==============================================================================

//------------------------------------------------------------------------------
// CHOLMOD/Partition:
// Copyright (C) 2005-2023, Univ. of Florida.  Author: Timothy A. Davis
//------------------------------------------------------------------------------

// CHOLMOD Partition module, interface to CAMD, CCOLAMD, CSYMAMD, and METIS,
// and graph partitioning and graph-partition-based orderings.  Includes an
// interface to CCOLAMD and CSYMAMD, constrained minimum degree ordering
// methods which order a matrix following constraints determined via nested
// dissection.
//
// These functions do not require METIS.  They are installed unless NCAMD
// is defined:
// cholmod_ccolamd      interface to CCOLAMD ordering
// cholmod_csymamd      interface to CSYMAMD ordering
// cholmod_camd         interface to CAMD ordering
//
// These functions require METIS:
// cholmod_nested_dissection    CHOLMOD nested dissection ordering
// cholmod_metis                METIS nested dissection ordering (METIS_NodeND)
// cholmod_bisect               graph partitioner (currently based on METIS)
// cholmod_metis_bisector       direct interface to METIS_ComputeVertexSeparator
//
// Requires the Utility and Cholesky modules, and three packages: METIS, CAMD,
// and CCOLAMD.  Optionally used by the Cholesky module.

#ifndef NCAMD

//------------------------------------------------------------------------------
// cholmod_ccolamd
//------------------------------------------------------------------------------

// Order AA' or A(:,f)*A(:,f)' using CCOLAMD.

int cholmod_ccolamd
(
    // input:
    cholmod_sparse *A,  // matrix to order
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int32_t *Cmember,   // size A->nrow.  Cmember [i] = c if row i is in the
                        // constraint set c.  c must be >= 0.  The # of
                        // constraint sets is max (Cmember) + 1.  If Cmember is
                        // NULL, then it is interpretted as Cmember [i] = 0 for
                        // all i.
    // output:
    int32_t *Perm,      // size A->nrow, output permutation
    cholmod_common *Common
) ;
int cholmod_l_ccolamd (cholmod_sparse *, int64_t *, size_t, int64_t *,
    int64_t *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_csymamd
//------------------------------------------------------------------------------

// Order A using CSYMAMD.

int cholmod_csymamd
(
    // input:
    cholmod_sparse *A,  // matrix to order
    // output:
    int32_t *Cmember,   // size nrow.  see cholmod_ccolamd.c for description
    int32_t *Perm,      // size A->nrow, output permutation
    cholmod_common *Common
) ;
int cholmod_l_csymamd (cholmod_sparse *, int64_t *, int64_t *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_camd: order A using CAMD
//------------------------------------------------------------------------------

int cholmod_camd
(
    // input:
    cholmod_sparse *A,  // matrix to order
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int32_t *Cmember,   // size nrow.  see cholmod_ccolamd.c for description.
    // output:
    int32_t *Perm,      // size A->nrow, output permutation
    cholmod_common *Common
) ;
int cholmod_l_camd (cholmod_sparse *, int64_t *, size_t, int64_t *, int64_t *,
    cholmod_common *) ;

#endif

//------------------------------------------------------------------------------
// CHOLMOD:Partition Module (graph partition methods)
//------------------------------------------------------------------------------

// These routines still exist if CHOLMOD is compiled with -DNPARTITION,
// but they return Common->status = CHOLMOD_NOT_INSTALLED in that case.

#if 1

//------------------------------------------------------------------------------
// cholmod_nested_dissection
//------------------------------------------------------------------------------

// Order A, AA', or A(:,f)*A(:,f)' using CHOLMOD's nested dissection method
// (METIS's node bisector applied recursively to compute the separator tree
// and constraint sets, followed by CCOLAMD using the constraints).  Usually
// finds better orderings than METIS_NodeND, but takes longer.

int64_t cholmod_nested_dissection  // returns # of components, or -1 if error
(
    // input:
    cholmod_sparse *A,  // matrix to order
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    // output:
    int32_t *Perm,      // size A->nrow, output permutation
    int32_t *CParent,   // size A->nrow.  On output, CParent [c] is the parent
                        // of component c, or EMPTY if c is a root, and where
                        // c is in the range 0 to # of components minus 1
    int32_t *Cmember,   // size A->nrow.  Cmember [j] = c if node j of A is
                        // in component c
    cholmod_common *Common
) ;
int64_t cholmod_l_nested_dissection (cholmod_sparse *, int64_t *, size_t,
    int64_t *, int64_t *, int64_t *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_metis
//------------------------------------------------------------------------------

// Order A, AA', or A(:,f)*A(:,f)' using METIS_NodeND.

int cholmod_metis
(
    // input:
    cholmod_sparse *A,  // matrix to order
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int postorder,      // if TRUE, follow with etree or coletree postorder
    // output:
    int32_t *Perm,      // size A->nrow, output permutation
    cholmod_common *Common
) ;
int cholmod_l_metis (cholmod_sparse *, int64_t *, size_t, int, int64_t *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_bisect
//------------------------------------------------------------------------------

// Finds a node bisector of A, A*A', A(:,f)*A(:,f)'.

int64_t cholmod_bisect  // returns # of nodes in separator
(
    // input:
    cholmod_sparse *A,  // matrix to bisect
    int32_t *fset,      // subset of 0:(A->ncol)-1
    size_t fsize,       // size of fset
    int compress,       // if TRUE, compress the graph first
    // output:
    int32_t *Partition, // size A->nrow.  Node i is in the left graph if
                        // Partition [i] = 0, the right graph if 1, and in the
                        // separator if 2.
    cholmod_common *Common
) ;
int64_t cholmod_l_bisect (cholmod_sparse *, int64_t *, size_t, int, int64_t *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_metis_bisector
//------------------------------------------------------------------------------

// Find a set of nodes that bisects the graph of A or AA' (direct interface
// to METIS_ComputeVertexSeperator).

int64_t cholmod_metis_bisector      // returns separator size
(
    // input:
    cholmod_sparse *A,  // matrix to bisect
    int32_t *Anw,       // size A->nrow, node weights, can be NULL,
                        // which means the graph is unweighted.
    int32_t *Aew,       // size nz, edge weights (silently ignored).
                        // This option was available with METIS 4, but not
                        // in METIS 5.  This argument is now unused, but
                        // it remains for backward compatibilty, so as not
                        // to change the API for cholmod_metis_bisector.
    // output:
    int32_t *Partition, // size A->nrow
    cholmod_common *Common
) ;
int64_t cholmod_l_metis_bisector (cholmod_sparse *, int64_t *, int64_t *,
    int64_t *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_collapse_septree
//------------------------------------------------------------------------------

// Collapse nodes in a separator tree.

int64_t cholmod_collapse_septree
(
    // input:
    size_t n,           // # of nodes in the graph
    size_t ncomponents, // # of nodes in the separator tree (must be <= n)
    double nd_oksep,    // collapse if #sep >= nd_oksep * #nodes in subtree
    size_t nd_small,    // collapse if #nodes in subtree < nd_small
    // output:
    int32_t *CParent,   // size ncomponents; from cholmod_nested_dissection
    int32_t *Cmember,   // size n; from cholmod_nested_dissection
    cholmod_common *Common
) ;
int64_t cholmod_l_collapse_septree (size_t, size_t, double, size_t, int64_t *,
    int64_t *, cholmod_common *) ;

#endif

//==============================================================================
// CHOLMOD:Supernodal Module
//==============================================================================

#ifndef NSUPERNODAL

// Supernodal analysis, factorization, and solve.  The simplest way to use
// these routines is via the Cholesky module.  It does not provide any
// fill-reducing orderings, but does accept the orderings computed by the
// Cholesky module.  It does not require the Cholesky module itself, however.
//
// Primary routines:
// -----------------
// cholmod_super_symbolic       supernodal symbolic analysis
// cholmod_super_numeric        supernodal numeric factorization
// cholmod_super_lsolve         supernodal Lx=b solve
// cholmod_super_ltsolve        supernodal L'x=b solve
//
// Prototypes for the BLAS and LAPACK routines that CHOLMOD uses are listed
// below, including how they are used in CHOLMOD.  Only the double methods are
// listed, but CHOLMOD also uses the corresponding single, single complex, and
// double complex routines.
//
// BLAS routines:
// --------------
// dtrsv    solve Lx=b or L'x=b, L non-unit diagonal, x and b stride-1
// dtrsm    solve LX=B or L'X=b, L non-unit diagonal
// dgemv    y=y-A*x or y=y-A'*x (x and y stride-1)
// dgemm    C=A*B', C=C-A*B, or C=C-A'*B
// dsyrk    C=tril(A*A'), zherk for the double complex case
//
// LAPACK routines:
// ----------------
// dpotrf   LAPACK: A=chol(tril(A))
//
// Requires the Utility module, and two external packages: LAPACK and the BLAS.
// Optionally used by the Cholesky module.

//------------------------------------------------------------------------------
// cholmod_super_symbolic
//------------------------------------------------------------------------------

// Analyzes A, AA', or A(:,f)*A(:,f)' in preparation for a supernodal numeric
// factorization.  The user need not call this directly; cholmod_analyze is
// a "simple" wrapper for this routine.

int cholmod_super_symbolic 
(
    // input:
    cholmod_sparse *A,  // matrix to analyze
    cholmod_sparse *F,  // F = A' or A(:,f)'
    int32_t *Parent,    // elimination tree
    // input/output:
    cholmod_factor *L,  // simplicial symbolic on input,
                        // supernodal symbolic on output
    cholmod_common *Common
) ;
int cholmod_l_super_symbolic (cholmod_sparse *, cholmod_sparse *, int64_t *,
    cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_super_symbolic2
//------------------------------------------------------------------------------

// Analyze for supernodal Cholesky or multifrontal QR

#define CHOLMOD_ANALYZE_FOR_SPQR     0
#define CHOLMOD_ANALYZE_FOR_CHOLESKY 1
#define CHOLMOD_ANALYZE_FOR_SPQRGPU  2

int cholmod_super_symbolic2
(
    // input:
    int for_whom,       // FOR_SPQR     (0): for SPQR but not GPU-accelerated
                        // FOR_CHOLESKY (1): for Cholesky (GPU or not)
                        // FOR_SPQRGPU  (2): for SPQR with GPU acceleration
    cholmod_sparse *A,  // matrix to analyze
    cholmod_sparse *F,  // F = A' or A(:,f)'
    int32_t *Parent,    // elimination tree
    // input/output:
    cholmod_factor *L,  // simplicial symbolic on input,
                        // supernodal symbolic on output
    cholmod_common *Common
) ;
int cholmod_l_super_symbolic2 (int, cholmod_sparse *, cholmod_sparse *,
    int64_t *, cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_super_numeric
//------------------------------------------------------------------------------

// Computes the numeric LL' factorization of A, AA', or A(:,f)*A(:,f)' using
// a BLAS-based supernodal method.  The user need not call this directly;
// cholmod_factorize is a "simple" wrapper for this routine.

int cholmod_super_numeric
(
    // input:
    cholmod_sparse *A,  // matrix to factorize
    cholmod_sparse *F,  // F = A' or A(:,f)'
    double beta [2],    // beta*I is added to diagonal of matrix to factorize
    // input/output:
    cholmod_factor *L,  // factorization
    cholmod_common *Common
) ;
int cholmod_l_super_numeric (cholmod_sparse *, cholmod_sparse *, double [2],
    cholmod_factor *, cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_super_lsolve
//------------------------------------------------------------------------------

// Solve Lx=b where L is from a supernodal numeric factorization.  The user
// need not call this routine directly.  cholmod_solve is a "simple" wrapper
// for this routine.

int cholmod_super_lsolve
(
    // input:
    cholmod_factor *L,  // factor to use for the forward solve
    // input/output:
    cholmod_dense *X,   // b on input, solution to Lx=b on output
    // workspace:
    cholmod_dense *E,   // workspace of size nrhs*(L->maxesize)
    cholmod_common *Common
) ;
int cholmod_l_super_lsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *,
    cholmod_common *) ;

//------------------------------------------------------------------------------
// cholmod_super_ltsolve
//------------------------------------------------------------------------------

// Solve L'x=b where L is from a supernodal numeric factorization.  The user
// need not call this routine directly.  cholmod_solve is a "simple" wrapper
// for this routine.

int cholmod_super_ltsolve
(
    // input:
    cholmod_factor *L,  // factor to use for the backsolve
    // input/output:
    cholmod_dense *X,   // b on input, solution to L'x=b on output
    // workspace:
    cholmod_dense *E,   // workspace of size nrhs*(L->maxesize)
    cholmod_common *Common
) ;
int cholmod_l_super_ltsolve (cholmod_factor *, cholmod_dense *, cholmod_dense *,
    cholmod_common *) ;

#endif

#ifdef __cplusplus
}
#endif

//==============================================================================
// CHOLMOD:SupernodalGPU Module
//==============================================================================

//------------------------------------------------------------------------------
// cholmod_score_comp: for sorting descendant supernodes with qsort
//------------------------------------------------------------------------------

#ifdef __cplusplus
extern "C" {
#endif

typedef struct cholmod_descendant_score_t
{
    double score ;
    int64_t d ;
}
descendantScore ;

int cholmod_score_comp   (struct cholmod_descendant_score_t *i,
                          struct cholmod_descendant_score_t *j) ;
int cholmod_l_score_comp (struct cholmod_descendant_score_t *i,
                          struct cholmod_descendant_score_t *j) ;

#ifdef __cplusplus
}
#endif

//------------------------------------------------------------------------------
// remainder of SupernodalGPU Module
//------------------------------------------------------------------------------

#ifdef CHOLMOD_HAS_CUDA

#include "omp.h"
#include <fenv.h>
#ifndef SUITESPARSE_GPU_EXTERN_ON
#include <cuda.h>
#include <cuda_runtime.h>
#endif

// CHOLMOD_GPU_PRINTF: for printing GPU debug error messages
// #define CHOLMOD_GPU_PRINTF(args) printf args
#define CHOLMOD_GPU_PRINTF(args)

// define supernode requirements for processing on GPU
#define CHOLMOD_ND_ROW_LIMIT 256  /* required descendant rows */
#define CHOLMOD_ND_COL_LIMIT 32   /* required descendnat cols */
#define CHOLMOD_POTRF_LIMIT  512  /* required cols for POTRF & TRSM on GPU */

// # of host supernodes to perform before checking for free pinned buffers
#define CHOLMOD_GPU_SKIP     3

#define CHOLMOD_HANDLE_CUDA_ERROR(e,s) {if (e) {ERROR(CHOLMOD_GPU_PROBLEM,s);}}

#ifdef __cplusplus
extern "C" {
#endif

typedef struct cholmod_gpu_pointers
{
    double *h_Lx [CHOLMOD_HOST_SUPERNODE_BUFFERS] ;
    double *d_Lx [CHOLMOD_DEVICE_STREAMS] ;
    double *d_C ;
    double *d_A [CHOLMOD_DEVICE_STREAMS] ;
    void   *d_Ls ;
    void   *d_Map ;
    void   *d_RelativeMap ;

} cholmod_gpu_pointers ;

int cholmod_gpu_memorysize   // GPU memory size available, 1 if no GPU
(
    size_t         *total_mem,
    size_t         *available_mem,
    cholmod_common *Common
) ;

int cholmod_l_gpu_memorysize // GPU memory size available, 1 if no GPU
(
    size_t         *total_mem,
    size_t         *available_mem,
    cholmod_common *Common
) ;

int cholmod_gpu_probe   ( cholmod_common *Common ) ;
int cholmod_l_gpu_probe ( cholmod_common *Common ) ;

int cholmod_gpu_deallocate   ( cholmod_common *Common ) ;
int cholmod_l_gpu_deallocate ( cholmod_common *Common ) ;

int cholmod_gpu_start   ( cholmod_common *Common ) ;
int cholmod_l_gpu_start ( cholmod_common *Common ) ;

void cholmod_gpu_end   ( cholmod_common *Common ) ;
void cholmod_l_gpu_end ( cholmod_common *Common ) ;

int cholmod_gpu_allocate   ( cholmod_common *Common ) ;
int cholmod_l_gpu_allocate ( cholmod_common *Common ) ;

#ifdef __cplusplus
}
#endif

#endif

#endif

